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

Let $(M, F)$ be a geodesically forward complete Finsler manifold and $p \in M$ . We observe how the preimage of a curve in $M$ under exponential map at $p$ can behave in the tangent space $T_{p} M$ 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 $p \in M$ as the development of $M$ . We deal with isometry problems of Finsler manifolds and differentiability conditions of cut loci.

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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

Vol. 308, No. 1, 2020

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

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors