The Fermi Flow and its Application to Geometry

TL;DR

This paper introduces the Fermi flow concept for hypersurfaces in Riemannian manifolds, providing a unified, simple method to derive known geometric results and presenting new, stronger findings.

Contribution

It presents the Fermi flow as a novel tool for studying hypersurface geometry, unifying existing results and deriving new, stronger theorems with a simplified approach.

Findings

Unified derivation of known geometric results

Introduction of Fermi flow as a new analytical tool

New theorems with stronger conclusions

Abstract

We introduce the notion of Fermi flow for hypersurfaces in Riemannian manifolds. It turns out that this is a powerful tool to study the geometry of distance surfaces about a given initial hypersurface. Some of the results in this paper are known in one form or another, however the aim is to demonstrate how they can all be derived by the same method and proved in a very simple manner. In addition we obtain some new results and results that are stronger than those stated in the literature.