The Azimuthal equidistant projection for a Finsler manifold by the exponential map
Let \((M,F)\) be a geodesically forward complete Finsler manifold endowed with an empty boundary, and \(\exp_p\) be the \(M\)-valued exponential map on \(T_pM\), the tangent space at \(p\in M\). In a few words, let us state some results stated by the authors. They look at the behaviour of two curves \(\tilde{c}(s)\) and \(c(s)=\exp_p(\tilde{c}(s))\) for \(s\in[0,1]\) such that \(\tilde{c}(0)\) belongs to the tangent cut locus of \(p\) and to the first tangent conjugate locus. Then, they seek the relation that exists between the tangent vectors of \(\tilde{c}(s)\) and \(c(s)\) at zero. Also, the authors consider the limit of \(\exp^{-1}_p(c(s))\), as \(s\) approaches zero, for a curve \(c\) such that \(c(0)\) belongs to the cut locus of \(p\).
scientific article; zbMATH DE number 7291147
scientific article