The index of a geodesic in a Randers space and some remarks about the lack of regularity of the energy functional of a Finsler metric

Caponio, Erasmo (2010) The index of a geodesic in a Randers space and some remarks about the lack of regularity of the energy functional of a Finsler metric. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 26 (2). pp. 265-274. ISSN 0866-0174

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Abstract

In a series of papers ([2, 3, 4]) the relations existing between the metric properties of Randers spaces and the conformal geometry of stationary Lorentzian manifolds were discovered and investigated. These relations were called in [4] \emph{Stationary-to-Randers Correspondence (SRC)}. In this paper we focus on one aspect of SRC, the equality between the index of a geodesic in a Randers space and that of its lightlike lift in the associated conformal stationary spacetime. Moreover we make some remarks about regularity of the energy functional of a Finsler metric on the infinite dimensional manifold of $H^1$ curves connecting two points, in connection with infinite dimensional techniques in Morse Theory.

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