Splitting lemmas for the Finsler energy functional on the space of $H^1$-curves

Guangcun Lu

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arXiv · 1411.3209

Splitting lemmas for the Finsler energy functional on the space of $H^1$-curves

Guangcun Lu

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Abstract

We establish the splitting lemmas (or generalized Morse lemmas) for the energy functionals of Finsler metrics on the natural Hilbert manifolds of $H^1$-curves around a critical point or a critical $\R^1$ orbit of a Finsler isometry invariant closed geodesic. They are the desired generalization on Finsler manifolds of the corresponding Gromoll-Meyer's splitting lemmas on Riemannian manifolds (\cite{GM1, GM2}). As an application we extend to Finsler manifolds a result by Grove and Tanaka \cite{GroTa78, Tan82} about the existence of infinitely many, geometrically distinct, isometry invariant closed geodesics on a closed Riemannian manifold.

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BibTeX RIS

Guangcun Lu. 2014-11-12. Splitting lemmas for the Finsler energy functional on the space of $H^1$-curves. https://arxiv.org/abs/1411.3209

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