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

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 ${\mathbb{S}}^n$, 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 ${\mathbb{S}}^n$ with a parallel Blaschke tensor. For proving this classification, some new kinds of examples are first defined.

Submitted

References in corpus (1)

• Möbius and Laguerre geometry of Dupin Hypersurfaces