On the immersed submanifolds in the unit sphere with parallel Blaschke tensor
Xingxiao Li, Hongru Song

TL;DR
This paper classifies immersed umbilic-free submanifolds in the unit sphere with a parallel Blaschke tensor, introducing new examples and advancing the understanding of M"obius invariants in differential geometry.
Contribution
It provides a classification theorem for such submanifolds and introduces new examples, enriching the study of Blaschke tensors in M"obius geometry.
Findings
Classification theorem for submanifolds with parallel Blaschke tensor
Introduction of new examples of such submanifolds
Deeper understanding of M"obius invariants in differential geometry
Abstract
As is known, the Blaschke tensor (a symmetric covariant -tensor) is one of the fundamental M\"obius invariants in the M\"obius differential geometry of submanifolds in the unit sphere , and the eigenvalues of are referred to as the Blaschke eigenvalues. In this paper, we shall prove a classification theorem for immersed umbilic-free submanifolds in with a parallel Blaschke tensor. For proving this classification, some new kinds of examples are first defined.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Geometry and complex manifolds
