Holonomy of K-contact sub-Riemannian manifolds

IF 0.9 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2025-10-13 DOI:10.1007/s10231-025-01612-w

Anton S. Galaev

引用次数: 0

Abstract

It is shown that the horizontal holonomy group of a K-contact sub-Riemannian manifold either coincides with the holonomy group of a Riemannian manifold, or it is a codimension-one normal subgroup of the later group. This implies the classification of the holonomy algebras of K-contact sub-Riemannian manifolds. The question of existence of parallel horizontal spinors, examples, and consequences are discussed.

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k -接触子黎曼流形的完整性

证明了k -接触子黎曼流形的水平完整群要么与黎曼流形的完整群重合，要么是后者群的余维一正规子群。这暗示了k -接触子黎曼流形的完整代数的分类。讨论了平行水平旋量的存在性问题、例子和结果。

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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来源期刊

Annali di Matematica Pura ed Applicata 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

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