#### 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 $\left(M,F\right)$ 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.

##### Keywords
Finsler manifold, cut locus, azimuthal equidistant projection, exponential map
Primary: 53C20
Secondary: 53C22