Symmetric spaces rolling on flat spaces

2022/05/29 by V. Jurdjevic, Jurdjevic, V., I. Markina +3 · 1 citation
Mathematics · #53A35 #53B21 #53C17 #53C25 #53C50 #Differential Geometry (math.DG) #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications #Point processes and geometric inequalities #Primary: 53C35 #Secondary: 53A17

paper · pdf · doi:10.48550/arxiv.2205.14636

openalex publication_date 2022/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The objective of the current paper is essentially twofold. Firstly, to make clear the difference between two notions of rolling a Riemannian manifold over another, using a language accessible to a wider audience, in particular to readers with interest in applications. Secondly, we concentrate on rolling an important class of Riemannian manifolds. In the first part of the paper, the relation between intrinsic and extrinsic rollings is explained in detail, while in the second part we address rollings of symmetric spaces on flat spaces and complement the theoretical results with illustrative examples.

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