Jacobi fields and conjugate points for a projective class of sprays

Abstract

We investigate Jacobi fields and conjugate points in the context of sprays. We first prove that the conjugate points of a spray remain preserved under a projective change. Then, we establish conditions on the projective factor so that the projectively deformed spray meets the conditions of a proposition that ensures the existence of conjugate points. We discuss our methods by means of illustrative examples, throughout the paper.

18 pages, 3 figures

References in corpus (3)

• The multiplier approach to the projective Finsler metrizability problem
• Conjugate points for systems of second-order ordinary differential equations
• Invariant metrizability and projective metrizability on Lie groups and homogeneous spaces