Vol. 308, No. 1, 2020

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The azimuthal equidistant projection for a Finsler manifold by the exponential map

Nobuhiro Innami, Yoe Itokawa, Toshiki Kondo, Tetsuya Nagano and Katsuhiro Shiohama

Vol. 308 (2020), No. 1, 73–101
Abstract

Let (M,F) be a geodesically forward complete Finsler manifold and p M. We observe how the preimage of a curve in M under exponential map at p can behave in the tangent space TpM at p, when the curve approaches a conjugate cut point of p without crossing the cut locus of p. After this investigation, we may regard the internal region of a tangent cut locus of p M as the development of M. We deal with isometry problems of Finsler manifolds and differentiability conditions of cut loci.

Keywords
Finsler manifold, cut locus, azimuthal equidistant projection, exponential map
Mathematical Subject Classification 2010
Primary: 53C20
Secondary: 53C22
Milestones
Received: 4 November 2019
Accepted: 27 May 2020
Published: 3 December 2020
Authors
Nobuhiro Innami
Department of Mathematics, Faculty of Science
Niigata University
Niigata
Japan
Yoe Itokawa
Department of Information and Communication Engineering
Fukuoka Institute of Technology
Wajiro-Higashi
Fukuoka
Japan
Toshiki Kondo
Graduate School of Science and Technology
Niigata University
Niigata
Japan
Tetsuya Nagano
Department of Information Security
University of Nagasaki
Nagasaki
Japan
Katsuhiro Shiohama
Fukuoka Institute of Technology
Wajiro-Higashi
Fukuoka
Japan