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
Abstract
In some recent papers, the relations existing between the metric properties of Randers spaces and the conformal geometry of stationary Lorentzian manifolds were discovered and investigated. In this note, we focus on 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 H1 curves between two points, in connection with infinite dimensional techniques in Morse Theory.
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