克莱沃公式的推广及其应用

arXiv - MATH - Differential Geometry Pub Date : 2024-09-04 DOI:arxiv-2409.02895

Vadym Koval

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引用次数: 0

摘要

本文的主要目的是研究在子曼形体 $M\subset\mathbb{R}^n$ 上以涉及到 $M$ 的欧几里得距离的特定方式构造的曲线成为大地线的条件。我们还提出了将主要结果推广到更高维度所需的克拉劳特公式的自然推广。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A generalization of Clairaut's formula and its applications

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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arXiv - MATH - Differential Geometry

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