A complete classification of Blaschke parallel submanifolds with vanishing M(o)bius form

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2017,（7）
• 页码范围: 1281-1310
• 页数: 30页
• 语种: 英文
• DOI: 10.1007/s11425-016-0174-y

摘要

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