English

A generalization of Clairaut's formula and its applications

Differential Geometry 2024-09-05 v1

Abstract

The main purpose of this article is to study conditions for a curve on a submanifold MRnM\subset\mathbb{R}^n, constructed in a particular way involving the Euclidean distance to MM, to be a geodesic. We also present the naturally arising generalization of Clairaut's formula needed for the generalization of the main result to higher dimensions.

Keywords

Cite

@article{arxiv.2409.02895,
  title  = {A generalization of Clairaut's formula and its applications},
  author = {Vadym Koval},
  journal= {arXiv preprint arXiv:2409.02895},
  year   = {2024}
}
R2 v1 2026-06-28T18:34:20.552Z