An index theory for paths that are solutions of a class of strongly indefinite variational problems |
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Authors: | Paolo Piccione Daniel V. Tausk |
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Affiliation: | (1) Departamento de Matemática, Universidade de S ao Paulo, Brazil (e-mail: {piccione,tausk}@ime.usp.br) , BR |
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Abstract: | We generalize the Morse index theorem of [12,15] and we apply the new result to obtain lower estimates on the number of geodesics joining two fixed non conjugate points in certain classes of semi-Riemannian manifolds. More specifically, we consider semi-Riemannian manifolds admitting a smooth distribution spanned by commuting Killing vector fields and containing a maximal negative distribution for . In particular we obtain Morse relations for stationary semi-Riemannian manifolds (see [7]) and for the G?del-type manifolds (see [3]). Received: 4 April 2001 / Accepted: 27 September 2001 / Published online: 23 May 2002 The authors are partially sponsored by CNPq (Brazil) Proc. N. 301410/95 and N. 300254/01-6. Parts of this work were done during the visit of the two authors to the IMPA, Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil, in January and February 2001. The authors wish to express their gratitude to all Faculty and Staff of the IMPA for their kind hospitality. |
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Keywords: | Mathematics Subject Classification (2000): 53C22 53C50 58E05 58E10 |
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