4 papers
On the Focal Locus of Submanifolds of a Finsler Manifold
Aritra Bhowmick, Sachchidanand Prasad
In this article, we investigate the focal locus of closed (not necessarily compact) submanifolds in a forward complete Finsler manifold. The main goal is to show that the associate…
Hausdorff Stability of the Cut Locus Under -Perturbations of the Metric
Aritra Bhowmick, Jin-ichi Itoh, Sachchidanand Prasad
In this article, we prove the stability with respect to the Hausdorff metric of the cut locus of a point in a compact Riemannian manifold…
On manifolds homeomorphic to spheres
Somnath Basu, Sachchidanand Prasad
We prove a result analogous to Reeb's theorem in the context of Morse-Bott functions: if a closed, smooth manifold admits a Morse-Bott function having two critical submanifolds…
Distance from a Finsler Submanifold to its Cut Locus and the Existence of a Tubular Neighborhood
Aritra Bhowmick, Sachchidanand Prasad
In this article we prove that for a closed, not necessarily compact, submanifold of a possibly non-complete Finsler manifold , the cut time map is always positive. As a…