Other
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(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
Upper bounds for the critical values of
homology classes of loops,
accepted for publication: Manuscripta Math.
arXiv2203.14051
Two short
closed geodesics on a sphere of odd dimension,
Calc.Var.Partial Differ.Equ. 62, Article Number 89 (2023) (Open Access)
doi.org/10.1007/s00526-023-02433-6
arXiv2203.07896
The second
closed geodesic, the fundamental group, and generic Finsler
metrics,
Mathem. Zeitschr. 302 (2022) 629 - 640 (Open Access)
doi.org/10.1007/s00209-022-03062-z
arXiv2011.01909
(with Iskander A. Taimanov)
Closed
geodesics on connected sums and 3-manifolds,
J.
Differential Geom. 120 (2022) 557 - 573
doi.org/10.4310/jdg/1649953350
arXiv1809.04588
(with Iskander A. Taimanov)
Critical values of
homology classes of loops and positive curvature,
J. Differential
Geom. 119 (2021) 141 - 158
doi.org/10.4310/jdg/1631124316
arXiv1707.09618
Solitons of the midpoint mapping and affine
curvature,
J.Geom. 112 No. 1 (2021) Paper No. 7, 17 p. (Open Access)
doi.org/10.1007/s00022-020-00567-y
arXiv2007.14067
(with Christine Rademacher)
Bumpy metrics on spheres and minimal index
growth,
J. Fixed Point Theory
Appl. 19 (2017) 289-298
doi:10.1007/s11784-016-0354-4.,
arXiv:1608.01937[math.DG]
Solitons of discrete curve shortening,
Results.Math 71 (2017) 455-482,
doi:10.1007/s00025-016-0572-5
,
arXiv:1508.07274[math.DG]
(with Christine Rademacher)
Conformally Einstein product spaces,
Diff. Geom. Appl. 49 (2016) 65-96,
doi: 10.1016/j.difgeo.2016.07.005,
arXiv:1607.03332[math.DG]
(with Wolfgang Kühnel)
Conformally Einstein spaces revisited.
In: 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)
Resonance for loop homology of spheres.
(with Nancy Hingston)
J. Differential Geom. 93 (2013) 133--174 Article
arXiv
An equivariant CW complex for the free
loop space of a Finsler manifold.
In: 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
The second closed geodesic on Finsler
spheres of dimension n>2
Trans. American Math. Soc. 362 (2010) 1413-1421 DOI
arXiv
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
Einstein spaces with a conformal group
Results in Math. 56 (2009) 421 - 444
(special volume dedicated to Katsumi Nomizu)
(with Wolfgang Kühnel) DOI
PDF
The length of a shortest geodesic loop.
Compt. Rend. Acad. Sci. Paris Sér. I, 346 (2008) 763-765 arXiv
Conformal transformations of
pseudo-Riemannian manifolds.
In: Recent developments in
Pseudo-Riemannian geometry.
Eds.: D.Alekseevsky, H. Baum, ESI Lect. Math. Phys.
EMS Publ. House Zürich 2008
(with Wolfgang Kühnel) PDF
The second closed geodesic on complex
projective planes
Front. Math. China 3
(2008) 253-258 DOI
PDF
Liouville's theorem in conformal geometry
(with Wolfgang Kühnel)
J. Math. pures appl. 88 (2007) 251-260 (ESI-preprint 1862) PDF
A singularity theorem for twistor spinors.
Annales de l'Inst. Fourier, Grenoble 57 (2007) 1135-1159
(with F.Belgun, N.Ginoux) arXiv
Existence of closed geodesics on
positively curved Finsler manifolds.
Erg. Th. & Dyn. Syst.
27 (2007) 251-260 DOI
arXiv
Non-reversible Finsler metrics of positive
curvature.
In: 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
Conformal geometry of gravitational plane
waves.
Geom.Ded. 109 (2004) 175-188 DOI
PDF
(with Wolfgang Kühnel)
A sphere theorem for non-reversible
Finsler metrics.
Math. Ann. 328 (2004) 373-387DOI
PDF
Conformal Ricci collineations of
space-times.
Gen. Rel. Grav. 33 (2001) 1905-1914 PDF
(with Wolfgang Kühnel)
Asymptotically Euclidean ends of Ricci
flat manifolds, and conformal inversion.
Math. Nachr. 219 (2000) 125-134 PDF.
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)
Asymptotically Euclidean manifolds and
twistor spinors. Comm. Math. Phys. 196 (1998) 67-76 PS
(with Wolfgang Kühnel)
Essential conformal fields in
pseudo-Riemannian geometry, II.
J. Math. Sci. Univ. Tokyo 4 (1997) 649--662
(with Wolfgang Kühnel)
Twistor spinors on conformally flat
manifolds.
Illinois J. Math. 41 (1997) 495-503
(with Wolfgang Kühnel)
Conformal vector fields on
pseudo-Riemannian spaces.
Diff.Geom. Appl. 7 (1997) 237-250
(with Wolfgang Kühnel)
Conformal completion of U(n)-invariant
Ricci-flat Kähler metrics at infinity.
Zeitschr. Anal. Anw. 16 (1997) 113-117
(with Wolfgang Kühnel)
Oscillator and pendulum equation on
pseudo-Riemannian spaces.
Tôhoku Math. J. 48 (1996) 601-612
(with Wolfgang Kühnel)
Oscillator and pendulum equation on
pseudo-Riemannian manifolds,
and conformal vector fields.
In: 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)
Twistor spinors and gravitational
instantons.
Lett. Math. Phys. 38 (1996) 411-419
(with Wolfgang Kühnel)
Essential conformal fields in
pseudo-Riemannian geometry.
J. Math. pures appl. 74 (1995) 453-481
(with Wolfgang Kühnel) PDF
Conformal diffeomorphisms preserving the
Ricci tensor.
Proc. Amer. Math. Soc. 123 (1995) 2841-2848
(with Wolfgang Kühnel)
Twistor spinors with zeros.
Intern. J. Math. 5 (1994) 877-895
(with Wolfgang Kühnel)
Twistor spinors with zeros and conformal
flatness.
Compt. Rend. Acad. Sci. Paris Sér. I 318 (1994) 237-240
(with Wolfgang Kühnel)
The Fadell-Rabinowitz index and closed
geodesics.
J. London Math. Soc. 50 (1994) 609-624 DOI PDF
On a generic property of geodesic flows.
Math. Ann. 298 (1994) 101-116 PDF
Morse-Theorie und Geschlossene Gedätische.
Habilitationsschrift, Bonn 1991 = Bonner
Math. Schr. 229 (1992) PDF
Generalized Killing spinors with imaginary
Killing function
and conformal Killing fields. PDF
In: Global Differential Geometry
and Global Analysis, Proc. Berlin 1990,
Springer Lect. Notes Math. 1481
(1991) 192-198
On the number of closed geodesics on the
2-torus.
Arch. Math. 56 (1991) 386-393
Metrics with only finitely many isometry
invariant geodesics.
Math. Ann. 284 (1989) 391-407
On the average indices of closed
geodesics.
J. Diff. Geom. 29 (1989) 65-83 Project
Euclid
On the equivariant Morse chain complex of
the space of closed curves.
Math. Zeitschr. 201 (1989) 279-302
Conformal and isometric immersions of
conformally flat Riemannian manifolds
into spheres and Euclidean spaces.
In: Conformal Geometry. Eds.: R.S.Kulkarni, U.Pinkall. Aspects Math. E
12,
Vieweg Verlag Braunschweig (1988) 191-216
Der Äquivariante Morse-Kettenkomplex des
Raums der geschlossenen Kurven.
Dissertation Bonn 1986 = Bonner
Math. Schr. 178 (1987)
On the number of closed geodesics on
projective spaces.
Math. Zeitschr. 186 (1984) 265-271
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
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