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On K-contact manifolds with minimal number
of closed characteristics

Author: Philippe Rukimbira
Journal: Proc. Amer. Math. Soc. 127 (1999), 3345-3351
MSC (1991): Primary 58F05, 58F22; Secondary 53C15, 53C57
Published electronically: May 3, 1999
MathSciNet review: 1646205
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that closed simply connected K-contact manifolds with minimal number of closed characteristics are homeomorphic to odd-dimensional spheres.

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  • [ABE] Abe, K. and Erbacher, J., Nonregular contact structures on Brieskorn manifolds, Bull. Amer. Math. Soc. 81 (1975), 407-409. MR 54:6019
  • [BLA] Blair, D., Contact manifolds in riemannian geometry, Springer Lectures Notes in Math, vol. 509, Springer Verlag, Berlin and New York, 1976. MR 57:7444
  • [BOT] Bott, R., Lectures on Morse Theory, old and new, Bulletin (New series) of the AMS 7 (1982), 331-358. MR 84m:58026a
  • [CAR] Carrière, Y., Flots riemanniens, Structures transverses des feuilletages, Astérisque 116 (1982), 31-52. MR 86m:58125a
  • [END] Endo, H., Invariant submanifolds in a contact riemannian manifold, Tensor (N.S.) 42 (1985), 86-89. MR 87e:53087
  • [GOL] Goldberg, S.I., Nonnegatively curved contact manifolds, Proc. Amer. Math. Soc. 96 (1986), 651-656. MR 87d:53068
  • [GST] Guillemin, V. and Sternberg, S., Convexity Properties of the Moment Mapping, Invent. math. 67 (1982), 491-513. MR 83m:58037
  • [PAO] Piu, P., Sur une charactérisation de la sphère $\mathbf{ S}^{2n+1}$ en termes de géométrie riemannienne de contact, Rendic. Cir. Math. Pal. Tomo XXXVIII (1989), 297-304.
  • [RU1] Rukimbira, P., Topology and closed characteristics on K-contact manifolds, Bull. Belg. Math. Soc. 2 (1995), 349-356. MR 96g:53044
  • [RU2] Rukimbira, P., Chern-Hamilton conjecture and K-contactness, Houston J. Math. 21 (1995), 709-718. MR 96m:53032
  • [RU3] Rukimbira, P., Some remarks on R-contact flows, Ann. Global Analy. Geom. 11, no 3 (1993), 165-171. MR 94h:53043
  • [SMA] Smale, S., The generalized Poincaré conjecture in higher dimensions, Bull. Amer. Math. Soc. (N.S.) 66 (1960), 373-375. MR 23:A2220
  • [WAD] Wadsley, A.W., Geodesic foliations by circles, J. Diff. Geom. 10 (1975), 541-549. MR 53:4092
  • [XIA] Xia, C., A generalization of the classical sphere theorem, Proc. Amer. Math. Soc. 125 (1997), 255-258. MR 98h:53059

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Additional Information

Philippe Rukimbira
Affiliation: Department of Mathematics, Florida International University, Miami, Florida 33199

Keywords: K-contact form, clean function, closed characteristics
Received by editor(s): May 9, 1997
Received by editor(s) in revised form: January 12, 1998
Published electronically: May 3, 1999
Communicated by: Christopher Croke
Article copyright: © Copyright 1999 American Mathematical Society

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