Hans-Bert Rademacher

Research Interests

(Pseudo-)Riemannian geometry, Finsler geometry, Conformal geometry, Dirac operators and twistor spinors,
Morse theory and closed geodesics, Topology of the free loop space, Discrete curve shortening


  1. Geodesic loops and orthogonal geodesic chords without self-intersections,


  1. Upper bounds for the critical values of homology classes of loops,
    manuscripta math. 174 (2024) 891-896
    (Open Access)
  2. Simple closed geodesics in dimensions >= 3,
    J. Fixed Point Theory Appl. (2024) (published online) (Open Access)
    SharedIt Link   
  3. Two short closed geodesics on a sphere of odd dimension,
    Calc.Var.Partial Differ.Equ. 62, Article Number 89 (2023)  (Open Access)

  4. The second closed geodesic, the fundamental group, and generic Finsler metrics,
    Mathem. Zeitschr. 302 (2022) 629 - 640 (Open Access)
    (with Iskander A. Taimanov)

  5. Closed geodesics on connected sums and 3-manifolds,
    J. Differential Geom. 120 (2022) 557 - 573
    (with Iskander A. Taimanov)

  6. Critical values of homology classes of loops and positive curvature,
    J. Differential Geom. 119 (2021) 141 - 158 


  7. Solitons of the midpoint mapping and affine curvature,
    112 No. 1 (2021) Paper No. 7, 17 p. (Open Access)

    (with Christine Rademacher)

  8. Bumpy metrics on spheres and minimal index growth,
    J. Fixed Point Theory Appl. 19 (2017) 289-298

  9. Solitons of discrete curve shortening,
    Results.Math 71 (2017) 455-482,
    (with Christine Rademacher)

  10. Conformally Einstein product spaces,
    Diff. Geom. Appl. 49 (2016) 65-96,
    doi: 10.1016/j.difgeo.2016.07.005

    (with Wolfgang Kühnel)

  11. Conformally Einstein spaces revisited.
    Pure and Applied Differential Geometry PADGE 2012, In Memory of Franki Dillen,
    J.Van der Veken, I.Van de Woestyne, L.Verstraelen, L.Vrancken (eds.),
    Shaker Verlag Aachen 2013, 161--167,
    (with Wolfgang Kühnel)

  12. Resonance for loop homology of spheres. (with Nancy Hingston)
    J. Differential Geom. 93 (2013) 133--174 Article arXiv

  13. An equivariant CW complex for the free loop space of a Finsler manifold.
    Progress in Variational Methods,
    Nankai Ser.Pure.Appl.Math. Theor.Phys., vol. 7,
    ed. by Chungen Liu and Yiming Long,
    Proc.Intern.Conf. on Variational Methods, Tianjin, May 2009,
    World Scientific, Singapore 2011, 187--194 PDF

  14. The second closed geodesic on Finsler spheres of dimension n>2
    Trans. American Math. Soc. 362 (2010) 1413-1421 DOI   arXiv

  15. Finsler conformal Lichnerowicz-Obata conjecture.
    (La conjecture de Lichnerowicz-Obata sur les transformations
    conformes des variétés Finslériennes).
    Annales Inst. Fourier 59 (2009) 937-949
    (with V.S.Matveev, M.Troyanov, A.Zehgib) DOI   arXiv

  16. Einstein spaces with a conformal group
    Results in Math. 56 (2009) 421 - 444
    (special volume dedicated to Katsumi Nomizu)
    (with Wolfgang Kühnel) DOI  PDF

  17. The length of a shortest geodesic loop.
    Compt. Rend. Acad. Sci. Paris Sér. I, 346 (2008) 763-765  arXiv

  18. Conformal transformations of pseudo-Riemannian manifolds.
    Recent developments in Pseudo-Riemannian geometry.
    Eds.: D.Alekseevsky, H. Baum, ESI Lect. Math. Phys.
    EMS Publ. House Zürich 2008
    (with Wolfgang Kühnel) PDF

  19. The second closed geodesic on complex projective planes
    Front. Math. China 3 (2008) 253-258 DOI PDF

  20. Liouville's theorem in conformal geometry (with Wolfgang Kühnel)
    J. Math. pures appl. 88 (2007) 251-260 (ESI-preprint 1862) PDF

  21. A singularity theorem for twistor spinors.
    Annales de l'Inst. Fourier, Grenoble 57 (2007) 1135-1159
    (with F.Belgun, N.Ginoux)  arXiv

  22. Existence of closed geodesics on positively curved Finsler manifolds.
    Erg. Th. & Dyn. Syst. 27 (2007) 251-260 DOI arXiv

  23. Non-reversible Finsler metrics of positive curvature.
    A sampler of Riemann-Finsler geometry.
    Eds.: D.Bao, R.Bryant, S.S.Chern, Z.Shen,
    Math.Sciences Res. Inst. Series 50, Cambridge Univ. Press 2004, 261-302

  24. Conformal geometry of gravitational plane waves.
    Geom.Ded. 109 (2004) 175-188 DOI  PDF
    (with Wolfgang Kühnel)

  25. A sphere theorem for non-reversible Finsler metrics.
    Math. Ann. 328 (2004) 373-387DOI PDF

  26. Conformal Ricci collineations of space-times.
    Gen. Rel. Grav. 33 (2001) 1905-1914 PDF
    (with Wolfgang Kühnel)

  27. Asymptotically Euclidean ends of Ricci flat manifolds, and conformal inversion.
    Math. Nachr. 219 (2000) 125-134  PDF.

  28. Conformal Killing fields in space times.
    Proc. Intl. Sem. Current topics in mathematical cosmology, Potsdam 1998.
    M.Rainer, H.J.Schmidt (eds.) World Scientific PC, Sinagpore 1999, 433-437
    (with Wolfgang Kühnel)

  29. Asymptotically Euclidean manifolds and twistor spinors. Comm. Math. Phys. 196 (1998) 67-76  PS
    (with Wolfgang Kühnel)

  30. Essential conformal fields in pseudo-Riemannian geometry, II.
    J. Math. Sci. Univ. Tokyo 4 (1997) 649--662
    (with Wolfgang Kühnel)

  31. Twistor spinors on conformally flat manifolds.
    Illinois J. Math. 41 (1997) 495-503
    (with Wolfgang Kühnel)

  32. Conformal vector fields on pseudo-Riemannian spaces.
    Diff.Geom. Appl. 7 (1997) 237-250
    (with Wolfgang Kühnel)

  33. Conformal completion of U(n)-invariant Ricci-flat Kähler metrics at infinity.
    Zeitschr. Anal. Anw. 16 (1997) 113-117
    (with Wolfgang Kühnel)

  34. Oscillator and pendulum equation on pseudo-Riemannian spaces.
    Tôhoku Math. J. 48 (1996) 601-612
    (with Wolfgang Kühnel)

  35. Oscillator and pendulum equation on pseudo-Riemannian manifolds,
    and conformal vector fields.
    Geometry and topology of submanifolds, VII,
    Differential geometry in honour of Katsumi Nomizu.
    Eds.: F.Dillen et al.,
    World Scientific Publ. Singapore (1995) 159-163
    (with Wolfgang Kühnel)

  36. Twistor spinors and gravitational instantons.
    Lett. Math. Phys. 38 (1996) 411-419
    (with Wolfgang Kühnel)

  37. Essential conformal fields in pseudo-Riemannian geometry.
    J. Math. pures appl. 74 (1995) 453-481
    (with Wolfgang Kühnel)  PDF

  38. Conformal diffeomorphisms preserving the Ricci tensor.
    Proc. Amer. Math. Soc. 123 (1995) 2841-2848
    (with Wolfgang Kühnel)

  39. Twistor spinors with zeros.
    Intern. J. Math. 5 (1994) 877-895
    (with Wolfgang Kühnel)

  40. Twistor spinors with zeros and conformal flatness.
    Compt. Rend. Acad. Sci. Paris Sér. I 318 (1994) 237-240
    (with Wolfgang Kühnel)

  41. The Fadell-Rabinowitz index and closed geodesics.
    J. London Math. Soc. 50 (1994) 609-624 DOI PDF

  42. On a generic property of geodesic flows.
    Math. Ann. 298 (1994) 101-116  PDF

  43. Morse-Theorie und Geschlossene Gedätische.
    Habilitationsschrift, Bonn 1991 = Bonner Math. Schr. 229 (1992) PDF

  44. Generalized Killing spinors with imaginary Killing function
    and conformal Killing fields.
    In: Global Differential Geometry and Global Analysis, Proc. Berlin 1990,
    Springer Lect. Notes Math.
    1481 (1991) 192-198

  45. On the number of closed geodesics on the 2-torus.
    Arch. Math. 56 (1991) 386-393

  46. Metrics with only finitely many isometry invariant geodesics.
    Math. Ann. 284 (1989) 391-407

  47. On the average indices of closed geodesics.
    J. Diff. Geom. 29 (1989) 65-83 Project Euclid

  48. On the equivariant Morse chain complex of the space of closed curves.
    Math. Zeitschr. 201 (1989) 279-302

  49. Conformal and isometric immersions of conformally flat Riemannian manifolds
    into spheres and Euclidean spaces.
    Conformal Geometry. Eds.: R.S.Kulkarni, U.Pinkall. Aspects Math. E 12,
    Vieweg Verlag Braunschweig (1988) 191-216

  50. Der Äquivariante Morse-Kettenkomplex des Raums der geschlossenen Kurven.
    Dissertation Bonn 1986 = Bonner Math. Schr. 178 (1987)

  51. On the number of closed geodesics on projective spaces.
    Math. Zeitschr. 186 (1984) 265-271

Editorial Work

  1. European Journal of Mathematics, Volume 3, Issue 4 (December 2017),
    Special issue:
    Finsler Geometry, New Methods and Perspectives
    Editors: Vladimir S. Matveev, Athanase Papdopoulos, Hans-Bert Rademacher,
    Sorin V. Sabau  Foreword


Slides of the talk Stringtopology and closed geodesics
Seminar Geometry, Topology and its Applications,
Novosibirsk (online) April, 19, 2021

Slides of the minicourse

Closed Geodesics and the Free Loop Space
Workshop on Symplectic Dynamics and Hamiltonian Systems
Chern Institute of Mathematics, Nankai Univ., Tianjin,
May 2014

zbMATH author ID (Zentralblatt MATH database)     Author ID: rademacher.hans-bert

MR Author ID (MathSciNet, Mathematical Reviews) : 203188



Version: 2024-07-08

ORCID iD icon https://orcid.org/0000-0002-0164-3660

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