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arXiv · 2409.02895

A generalization of Clairaut's formula and its applications

Vadym Koval
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Abstract

The main purpose of this article is to study conditions for a curve on a submanifold $M\subset\mathbb{R}^n$, constructed in a particular way involving the Euclidean distance to $M$, 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.

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Vadym Koval. 2024-09-04. A generalization of Clairaut's formula and its applications. https://arxiv.org/abs/2409.02895

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