This image shows Uwe Semmelmann

Uwe Semmelmann

Prof. Dr.

Professor - Chair for Geometry
Head of Examination Committee "Studies Teacher Education Mathematics"
Institute of Geometry and Topology
Chair for Geometry


Pfaffenwaldring 57
70550 Stuttgart
Room: 7.544

Office Hours

by appointment



Dirac operators on Riemannian manifolds, Killing spinors, Quaternion Kähler geometry, Weitzenböck formulae, Special structures in Differential Geometry, e.g. nearly Kähler manifolds, weak G2-manifolds, Sasakian manifolds, conformal Killing forms, extremal metrics.


  • Towards Brin's conjecture on frame flow ergodicity: new progress and perspectives
    (mit Mihajlo Cekić, Thibault Lefeuvre und Andrei Moroianu).
    [arxiv2204.08728], (2022)
    to appear in  Mathematics Research Reports

  • Stability of the Non-Symmetric Space E7/PSO(8)
    (mit Paul Schwahn und Gregor Weingart)
    [arXiv:2203.10138], (2022) 

  • On the ergodicity of the frame flow on even-dimensional manifolds,
    (with Mihajlo Cekic, Thibault Lefeuvre and Andrei Moroianu),
    [arXiv2111.14811], (2022)

  • Eigenvalue estimates for 3-Sasaki structures
    (mit Paul-Andi Nagy)

  • The G_2 geometry of 3-Sasaki structures
    (mit Paul-Andi Nagy)


Liste im: [arXiv] bzw im: [MSciN]

    1. Linear Instability of Sasaki Einstein and nearly parallel G2 manifolds
      to appear in Internat. J. Math.
      (mit Changliang Wang und McKenzie Wang)
    2. Conformal Killing forms in Kähler geometry,
      to appear in Illinois Journal of Mathematics
      (with Paul-Andi Nagy)
    3. Stability of Compact Symmetric Spaces,
      The Journal of Geometric Analysis 32 (2022) 32:137
      (with Gregor Weingart)
    4.  Deformations of nearly G2-structures,
      J. London Math. Soc. (2) 104 (2021) 1795–1811
      with Paul-Andi Nagy)
    5. Metric connections with parallel skew-symmetric torsion,
      Adv. Math. 378, 107519 (2021)
      (with Richard Cleyton, Andrei Moroianu)
    6. An Obata-type characterization of doubly-warped product Kähler manifolds,
      Münster J. Math. 14 (2021), no. 2, 295-321
      (with Nicolas Ginoux, Georges Habib, Mihaela Pilca)
    7. An Obata-type characterization of Calabi metrics on line bundles,
      North-West. Eur. J. Math. 6 (2020), 119-136 
      (with Nicolas Ginoux, Georges Habib, Mihaela Pilca)
    8. Conformal Killing forms on nearly Kähler manifolds,
      Differential Geom. Appl. 70 (2020), [arXiv:1903.06734]
      (with Antonio M. Naveira)
    9. On the linear stability of nearly Kähler 6-manifolds,
      Ann. Global Anal. Geom. 57 no. 1, 15-22 (2020), [arXiv:1907.12512]
      (with C. Wang and M. Wang).
    10. Generalized vector cross products and Killing forms on negatively curved manifolds,
      Geom. Dedicata 205 (1), 113-127 (2020), [arXiv:1806.06255]
      (with Laura Barberis and Andrej Moroianu)
    11. The kernel of the Rarita-Schwinger operator on Riemannian spin manifolds,
      Comm. Math. Phys. 370 no. 3, 853-871 (2019), [arXiv:1804.10602]
      (with Yasushi Homma)
    12. The Standard Laplace operator
      Manuscripta Math. 158, no. 1-2, 273-293 -8273-293, [arXiv:1708.04775]
      (with G. Weingart)
    13. Killing tensors on tori
      J. Geo. Phys. 117, 1-6 (2017), [arXiv:1610.02009]
      (with Konstantin Heil und Andrei Moroianu)
    14. Killing and Conformal Killing tensors
      J. Geom. Phys. 106, 383-400 (2016), [pdf]
      (with Konstantin Heil und Andrei Moroianu)
    15. Generalized Killing spinors and Lagrangian graphs
      Differ. Geom. Appl. 37 (2014), 141-151, [arXiv:1405.0838], [pdf]
      (with Andrei Moroianu)
    16. Generalized Killing spinors on Spheres
      Ann. Global Anal. Geom. 46 (2014), no. 2, 129-143, [arXiv:1310.0219], [pdf]
      (with Andrei Moroianu)
    17. Weakly complex homogeneous spaces
      J. reine angew. Math. 691 (2014), 229-244, [arXiv:1202.3363], [pdf]
      (with Andrei Moroianu)
    18. Generalized Killing spinors on Einstein manifolds
      Internat. J. Math. 25 (2014), no. 4, 1 - 19, [arXiv:1303.6179], [pdf]
      (with Andrei Moroianu)
    19. Homogeneous almost quaternion-Hermitian manifolds
      Math. Ann. 357 (2013), no. 4, 1205-121, [arXiv:1211.4383], [pdf]
      (with Andrei Moroianu und Mihaela Pilca)
    20. Invariant four-forms and symmetric pairs
      Ann. Global. Anal. Geom. 43, 107-121 (2013), [arXiv:1202.3407], [pdf]
      (with Andrei Moroianu)
    21. Extrinsic hyperspheres in manifolds with special holonomy
      Differ. Geom. Appl. 31, 104-111 (2013], [arXiv:1107.1603], [pdf]
      (with Andrei Moroianu und Tillmann Jentsch)
    22. Deformations of nearly parallel G_2-structures
      Asian Journal of Math. Vol. 16, No. 4, 713-744 (2012), [arXiv:1101.2143 ], [pdf]
      (with Bogdan Alexandrov)
    23. Imaginary Kählerian Killing spinors I
      Ann. Global Anal. Geom. 40, no. 4, 467--495 (2011), [arXiv:1102.4263], [pdf]
      (with Nicolas Ginoux)
    24. Clifford structures on Riemannian manifolds
      Adv. Math. 228, 940-967 (2011), [arXiv:0912.4207], [pdf]
      (with Andrei Moroianu)
    25. Almost complex structures on quaternion-Kähler manifolds and inner symmetric spaces,
      Invent. Math. 184, 389-403 (2011), [arXiv:1003.5172], [pdf]
      (with Andrei Moroianu und Paul Gauduchon)
    26. Infinitesimal Einstein deformations of nearly Kähler metrics,
      Trans. Amer. Math. Soc. 363, 3057-3069 (2011), [arXiv:0702455], [pdf]
      (with Andrei Moroianu)
    27. The Hermitian Laplace operator on nearly Kähler manifolds
      Commun. Math. Phys. 294, 251-272 (2010), [arXiv:0810.0164], [pdf]
      (with Andrei Moroianu)
    28. The Weitzenböck machine
      Compositio Math. 146, 2, 507-540 (2010), [arXiv:0702031], [pdf]
      (with Gregor Weingart)
    29. Deformations of nearly Kähler structures
      Pacific J. Math. 235, 57-72 (2008), [arXiv:0611223], [pdf]
      (with Andrei Moroianu und Paul-Andi Nagy)
    30. Killing forms on G2 and Spin7 manifolds
      J. Geom. Phys. 56 (2006) 1752-1766, [arXiv:0410065 ], [pdf].
    31. Killing forms on quaternion-Kähler manifolds
      Ann. Global Anal. Geom. 28, 319-335 (2005],
      erratum 34, 431-432 (2008), [arXiv:0403242], [pdf1], [pdf2]
      (with Andrei Moroianu)
    32. Killing forms on symmetric spaces
      Differential Geom. Appl. 24, 215-222 (2006), [arXiv:0409104], [pdf]
      (with Florin Belgun und Andrei Moroianu)
    33. Twistor forms on Riemannian products
      J. Geom. Phys. 58, 1343-1345 (2008), [arXiv:0407063], [pdf]
      (with Andrei Moroianu)
    34. Unit Killing vector fields on nearly Kähler manifolds
      Internat. J. Math. 16, 281-301 (2005), [arXiv:0406492], [pdf]
      (with Andrei Moroianu und Paul-Andi Nagy)
    35. An upper bound for a Hilbert polynomial on quaternionic Kähler manifolds
      J. Geom. Anal. 14 (2004), 151--170, [arXiv:0208079], [pdf]
      (with Gregor Weingart)
    36. Conformal Killing forms on Riemannian Manifolds
      Math. Z. 245 (2003), no. 3, 503--527, [arXiv:0206117], [pdf],
      Habilitationsschrift: pdf
    37. Twistor forms on Kähler manifolds
      Ann. Sc. Norm. Super. Pisa Cl. Sci. 2, 823-845 (2003), [arXiv:0204322], [pdf]
      (with Andrei Moroianu)
    38. Symmetries of contact metric manifolds
      Geometriae Dedicata 101, 203-216 (2003), [arXiv:0203090], [pdf]
      (with Florin Belgun und Andrei Moroianu)
    39. Scalar Curvature Estimates for Compact Symmetric Spaces
      Differential Geom. Appl. 16 (2002), no. 1, 65-78, [arXiv:/0010199], [pdf]
      (with Sebastian Goette)
    40. Vanishing Theorems for Quaternionic Kähler Manifolds
      J. Reine Angew. Math. 544 (2002), 111-132, [arXiv:/0001061], [pdf]
      (with Gregor Weingart)
    41. Spin^c Structures and Scalar Curvature Estimates
      Ann. Glob. Anal. Geom. , 20 (4):301-324 (2001), [arXiv:/9905089], [pdf]
      (with Sebastian Goette)
    42. The point spectrum of the Dirac operator on noncompact symmetric spaces
      Proc. Amer. Math. Soc. 130 (2002), no. 3, 915-923, [arXiv:/9903177], [pdf]
      (with Sebastian Goette)
    43. Parallel spinors and holonomy groups
      J. Math. Phys. 41, 2395-2402 (2000)], [arXiv:9903062], [pdf]
      (with Andrei Moroianu)
    44. Spinors, Self-Duality and IP Algebraic Curvature Tensors
      Proceedings of the Symposium on Contemporary Mathematics
      18-20 December 1998, Belgrade, Serbia
      (with Peter Gilkey)
    45. Eigenvalue estimates for the Dirac operator on quaternionic Kähler manifolds,
      Math. Z. 230, 4 (1999), 727--751, [pdf]
      (with Wolfram Kramer und Gregor Weingart)
    46. The First Eigenvalue of the Dirac Operator on Quaternionic Kähler Manifolds,
      Comm. Math. Phys. 199 (1998), 327-349, [arXiv:9709014], [pdf]
      (with Wolfram Kramer und Gregor Weingart)
    47. Quaternionic Killing spinors,
      Ann. Glob. Anal. Geom. 16 (1998), 63-87., [pdf]
      (with Wolfram Kramer und Gregor Weingart)
    48. A short proof of eigenvalue estimates for the Dirac operator on Riemannian and Kähler manifolds,
      Differential Geom. Appl., proceedings, Brno (1998), 137-140
    49. Killing spinors are Killing vector fields in Riemannian Supergeometry,
      J. Geom. Phys. 26 (1998), no. 1-2, 37--50,  [pdf]
      (with D.V. Alekseevsky, V. Cortes und C. Devchand)
    50. On nearly parallel G2-structures
      J. Geom. Phys. 23, 259-286 (1997), [hal-00126037], [pdf]
      (Thomas Friedrich, Ines Kath und Andrei Moroianu)
    51. Kählerian Killing spinors, complex contact structures and twistor spaces
      C. R. Acad. Sci. I Math. 323, 57-61 (1996), [pdf]
      (with Andrei Moroianu)
    52. Complex Contact Structures and the First Eigenvalue of the Dirac Operator on Kähler Manifolds,
      Geom. and Funct. Analysis 5 (1995), 604-618]
      (with Klaus-Dieter Kirchberg)
    53. Kählersche Killingspinoren und komplexe Kontaktstrukturen
      thesis, Humboldt Universität zu Berlin (1995)
    54. The Spectrum of the Dirac Operator on Complex Projective Spaces,
      SFB 288 preprint, no. 95, Berlin (1993)
      (with Sönke Seifarth)

SPP 2026 "Geometry at infinity!"

In the priority programme of the DFG SSP 2026 Prof. Uwe Semmelmann coordinates the projekt 15 "Spaces and Moduli Spaces of Riemannian Metrics with Curvature Bounds on compact and non-compact Manifolds".

The project concentrates on three major issues:

  • The space of positive scalar curvature metrics
  • Fiber bundles with geometric structures and spaces of Riemannian metrics
  • Moduli spaces for nonnegative sectional and positive Ricci curvature


DFG-Project SE933/5-1: "Rigidity, stability and deformations in nearly parallel

  • Principal Investigator: Prof. Uwe Semmelmann
  • Funding Period:  15.07.2020 bis 14.07.2023
  • Summary: This project studies various problems in nearly G2 geometry. There are three main directions proposed. First the stability of nearly G2 metrics among Einstein metrics shall be considered. Then the question whether or not nearly G2 structures are rigid is to be studied. This should include the study of the deformation theory for the second Einstein metric on 7-dimensional 3-Sasaki manifolds and finally the problem of the existence of deformations for associative submanifolds in nearly G2 geometry.

More information

Summer Term 2023:

  • Lecture Topologie
  • Seminar Der Laplace Operator

Winter Term 2022/2023:

  • Lecture HM3
  • Seminar Differentialgeometrie 

Sommer Term 2022:

  • Lecture Riemannsche Geometrie
  • Seminar  Einstein Metriken

Winter Term 2021/2022:

  • Lecture Differentialgeometrie
  • Seminar "Zahlen"

Sommer Term 2021:

  • Lecture Geometrie für das Lehramt
  • Lecture Topology

Summer Term 2020:

  • Lecture Spin-Geometrie und Dirac-Operatoren
  • Seminar Riemannsche Geometrie und Holonomie-Theorie

Winter Term 2019/2020

  • Lecture Kähler Mannigfaltigkeiten
  • Seminar Kalibrierte Geometrien
Summer Term 2019
  • Vorlesung Differentialoperatoren auf Mannigfaltigkeiten
  • Oberseminar Geometrie und Topologie
Winter Term 2018/2019
  • Lecture HM 3
  • Seminar: De Rham-Kohomologie
  • Seminar of the Institute
Summer Term 2018
  • Lecture Geometrie 
  • Seminar: Der Laplace-Operator auf Riemannschen Mannigfaltigkeiten
  • Seminar: Zahlen 
  • Seminar of the Insitute
Winter Term 2017/18
  • Lecture Topologie 
  • Seminar Zahlen WiSe 17/18
  • Seminar of the Insitute
Summer Term 2017
  • Lecture Geometrie 
  • Lecture Komplexe Geometrie A: Kähler Mannigfaltigkeiten
  • Seminar of the Insitute
Winter Term 2016/17
  • Lecture Differential-Geometrie
  • LectureIndex-Theorie 1 (Spingeometrie und Diracoperatoren)
  • Seminar of the Insitute
Winter Term 2015/17
  • Lecture Topologie
  • Seminar of the Insitute
Summer Term 2015
  • Lineare Algebra II (Skript und Glossar)
  • Seminar of the Insitute
Winter Term 2014/15
  • Lineare Algebra I
  • Seminar of the Insitute
Summer Term 2014
  • Spingeometrie und Diracoperatoren
  • Seminar of the Insitute
Winter Term 2013/2014
  • Lecture Differentialoperatoren auf Mannigfaltigkeiten
  • Seminar: Spin-Geometrie und Dirac-Operatoren
  • Seminar of the Insitute
Winter Term 2012/2013
  • Lecture Differential-Geometrie
  • Seminar: Lie-Gruppen und Darstellungstheorie
Summer Term 2012
  • Lecture Geometrie 
  • Proseminar: Gruppen und Symmetrien
  • Seminar: Hyperbolische Geometrie 
Summer Term 2011
  • Lecture Riemannsche Geometrie
  • Seminar-Zahlen
Winter Term 2010/2011
  • Lecture Differentialgeometrie

Homepage at the University of  Köln (until 2010)


  • Theorem von Seifert und van Kampen (2022)
  • Variationsrechnung in der Riemannschen Geometrie (2022)
  • Theorem of Seifert and van Kampen (2022)
  • Context and curvature in homogeneous spaces (2020)
  • Geometrically Formal Manifolds (2020)
  • Curvature of symmetrc spaces (21020)
  • Das Theorem von Obata (2019)
  • Die Hopf-Invariante (2019)
  • Die exzeptionelle Lie-Gruppe G2 (2018)
  • Die Hitchin-Thorpe-Ungleichung auf vierdimensionalen Einstein-Mannigfaltigkeiten (2018)
  • Orientierung von Mannigfaltigkeiten (2017)
  • Kähler-Geometrie von Flaggenmannigfaltigkeiten (2017)
  • Äquivalenzen 2-Punkt-homogener Räume (2015)
  • Minimalflächen(2014)
  • Geometrie der Hopf-Faserung (2014)
  • Einstein-Metriken auf Riemannschen Submersionen (2013)
  • Die Nearly Kähler Struktur der S6 (2013)


  • Einstein deformations on homogeneous spaces (2020)
  • Die Eguchi-Hanson Metrik (2019)


  • On the Lichnerowicz Laplace operator and its application to stability of spacetimes (2013)
  • Die Sasaki-Metrik auf dem Tangential- und dem Sphärenbündel (2011)
  • Lifting SU(3)-structures to nearly parallel G2-structures
  • Intrinsische Torsion und Ricci-Krümung von SU(3)-Strukturen (2006)
  • Das Spektrum des Diracoperators auf der Moufang-Ebene OP2 (2004)


  • Gruppen-Beispiele, Eigenschaften und Anwendungen (2020)
  • Gitter und ihre Anwendungen (2020)
  • Der Fundamentalsatz der Algebra (2019)
  • Ein Einblick in die Welt der tranzendierenden Zahlen (2019)
  • Divisionsalgebren und Vektorkreuzprodukte (2019)
  • Graphentheorie in der Schule (2018)
  • Geometirsche Axiomatik am Beispiel von affiner und hyperbolischer Geometrie (2014)
  • Theorie der Enveloppen und Anwendungen (2014)
  • Minimalflächen (2008)

Doctoral Degree

  • Paul Schwahn: Stability of Einstein Metrics on Homogeneous Spaces (2023)
  • Konstantin Heil:Killing and Conformal Killing Tensors (2017)
  • Sebastian Stock: Evolution of Geometries with Torsion (2010)
  • Christian Stromenger: Sasakian Manifolds: Differential Forms, Curvature and Conformal Killing Forms (2010)
  • Mihaela Pilca: Generalized Gradients of G-Structures and Kählerian Twistor Spinors (2009)
To the top of the page