A complete classification of Blaschke parallel submanifolds with vanishing Möbius form
Tóm tắt
The Blaschke tensor and the Möbius form are two of the fundamental invariants in the Möbius geometry of submanifolds; an umbilic-free immersed submanifold in real space forms is called Blaschke parallel if its Blaschke tensor is parallel. We prove a theorem which, together with the known classification result for Möbius isotropic submanifolds, successfully establishes a complete classification of the Blaschke parallel submanifolds in S
n
with vanishing Möbius form. Before doing so, a broad class of new examples of general codimensions is explicitly constructed.
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