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

Original · EN

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 Sⁿ, and the eigenvalues of A are referred to as the Blaschke eigenvalues. In this paper, we continue our job for the study on the submanifolds in ⁿ with parallel Blaschke tensors which we simply call Blaschke parallel submanifolds to find more examples and seek a complete classification finally. The main theorem of this paper is the classification of Blaschke parallel submanifolds in Sⁿ with exactly three distinct Blaschke eigenvalues. Before proving this classification we define, as usual, a new class of examples.