2014/11/12 by Guangcun Lu, Lu, Guangcun · 1 citation
Mathematics · Physics and Astronomy · #53B40 #53C20 #53C22 #58B20 #58E05 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #Energy (signal processing) #Energy functional #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometry and complex manifolds #Linguistics #Mathematical analysis #Mathematics #Philosophy #Pure mathematics #Space (punctuation) #Statistics #math.DG #math.DS #math.GT #msc:53B40 #msc:53C20 #msc:53C22 #msc:58B20 #msc:58E05
paper · pdf · doi:10.48550/arxiv.1411.3209
56 pages, Latex, latest version, to appear in Proceedings of the London Mathematical Society
openalex publication_date 2014/11/12 · arxiv created 2016/05/04 · arxiv updated 2016/05/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We establish the splitting lemmas (or generalized Morse lemmas) for the energy functionals of Finsler metrics on the natural Hilbert manifolds of H1-curves around a critical point or a critical \R1 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 (\citeGM1, GM2). As an application we extend to Finsler manifolds a result by Grove and Tanaka \citeGroTa78, Tan82 about the existence of infinitely many, geometrically distinct, isometry invariant closed geodesics on a closed Riemannian manifold.