Blaschke Finsler manifolds and actions of projective Randers changes on cut loci

Innami, Nobuhiro; Itokawa, Yoe; Nagano, Tetsuya; Shiohama, Katsuhiro

doi:10.1090/tran/7603

Blaschke Finsler manifolds and actions of projective Randers changes on cut loci
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by Nobuhiro Innami, Yoe Itokawa, Tetsuya Nagano and Katsuhiro Shiohama PDF

Trans. Amer. Math. Soc. 371 (2019), 7433-7450 Request permission

Abstract:

We study the cut and conjugate locus of a point in a complete Finsler manifold. Our study focuses on their intersection. We propose the Finsler version of Klingenberg’s lemma and determine the structure of the cut and conjugate locus in a Blaschke Finsler manifold. In order to have some examples, we study how cut and conjugate loci change under a projective Randers change. We see the relation between invariance of cut loci and exactness of a closed $1$-form in its projective Randers changes.

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