A complete classification of Blaschke parallel submanifolds with vanishing Möbius form
| Autor: | XingXiao Li, HongRu Song |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Class (set theory) Mathematics::Combinatorics Mathematics::Complex Variables General Mathematics Blaschke product 010102 general mathematics Mathematical analysis Isotropy Space (mathematics) Submanifold 01 natural sciences 010101 applied mathematics symbols.namesake Tensor (intrinsic definition) Classification result symbols Mathematics::Metric Geometry Mathematics::Differential Geometry 0101 mathematics Mathematics::Symplectic Geometry Mathematics |
| Zdroj: | Science China Mathematics. 60:1281-1310 |
| ISSN: | 1869-1862 1674-7283 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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