Transnormal Functions and Focal Varieties on Finsler Manifolds
Yali Chen, Qun He
TL;DR
This paper investigates the properties of transnormal functions on Finsler manifolds, showing that their focal varieties are smooth and that regular level sets form tubes over these focal varieties.
Contribution
It establishes the smoothness of focal varieties and describes the structure of level sets for transnormal functions on Finsler manifolds.
Findings
Focal varieties of transnormal functions are smooth submanifolds
Regular level sets are tubes over focal varieties
Provides geometric structure insights on Finsler manifolds
Abstract
In this paper, we study transnormal functions and their level sets and focal varieties on complete Finsler manifolds. We prove that the focal varieties of a C2 transnormal function are smooth submanifolds and each regular level set is a tube over either of the focal varieties.
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Taxonomy
TopicsAdvanced Differential Geometry Research · Fibroblast Growth Factor Research · Geometric Analysis and Curvature Flows