Ruled austere submanifolds of dimension four
| Autor: | Thomas A. Ivey, Marianty Ionel |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics Gauss map Ruled submanifolds Euclidean space Holomorphic function Primary 53B25 Secondary 53B35 53C38 58A15 Type (model theory) Austere submanifolds Generalized helicoid Connection (mathematics) Differential Geometry (math.DG) Computational Theory and Mathematics Grassmannian FOS: Mathematics Twistor space Exterior differential systems Mathematics::Differential Geometry Geometry and Topology Analysis Mathematics |
| Zdroj: | Differential Geometry and its Applications. 30:588-603 |
| ISSN: | 0926-2245 |
| DOI: | 10.1016/j.difgeo.2012.07.007 |
| Popis: | We classify 4-dimensional austere submanifolds in Euclidean space ruled by 2-planes. The algebraic possibilities for second fundamental forms of an austere 4-fold M were classified by Bryant, falling into three types which we label A, B, and C. We show that if M is 2-ruled of Type A, then the ruling map from M into the Grassmannian of 2-planes in R^n is holomorphic, and we give a construction for M starting with a holomorphic curve in an appropriate twistor space. If M is 2-ruled of Type B, then M is either a generalized helicoid in R^6 or the product of two classical helicoids in R^3. If M is 2-ruled of Type C, then M is either a one of the above, or a generalized helicoid in R^7. We also construct examples of 2-ruled austere hypersurfaces in R^5 with degenerate Gauss map. Comment: 20 pages |
| Databáze: | OpenAIRE |
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