On the immersed submanifolds in the unit sphere with parallel Blaschke tensor

2015/11/09 by Xingxiao Li, Li, Xingxiao, Hongru Song +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Primary 53A30 #Secondary 53B25 #math.DG #msc:53A30 #msc:53B25

paper · pdf · doi:10.48550/arxiv.1511.02560

Submitted

arxiv created 2015/12/03 · arxiv updated 2015/12/04

Abstract

As is known, the Blaschke tensor A (a symmetric covariant 2-tensor) is one of the fundamental Möbius invariants in the Möbius differential geometry of submanifolds in the unit sphere \mathbb Sⁿ, and the eigenvalues of A are referred to as the Blaschke eigenvalues. In this paper, we shall prove a classification theorem for immersed umbilic-free submanifolds in \mathbb Sⁿ with a parallel Blaschke tensor. For proving this classification, some new kinds of examples are first defined.

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