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 \((M,\frak{g})\) admitting a smooth distribution spanned by commuting Killing vector fields and containing a maximal negative distribution for \(\frak{g}\). In particular we obtain Morse relations for stationary semi-Riemannian manifolds (see [7]) and for the Gödel-type manifolds (see [3]).
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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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Piccione, P., Tausk, D. An index theory for paths that are solutions of a class of strongly indefinite variational problems. Calc Var 15, 529–551 (2002). https://doi.org/10.1007/s005260100136
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DOI: https://doi.org/10.1007/s005260100136