A complete classification of Blaschke parallel submanifolds with vanishing Möbius form

Abstract

The Blaschke tensor and the Mobius form are two of the fundamental invariants in the Mobius 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 Mobius isotropic submanifolds, successfully establishes a complete classification of the Blaschke parallel submanifolds in Sn with vanishing Mobius form. Before doing so, a broad class of new examples of general codimensions is explicitly constructed.