Totally complex submanifolds of a complex Grassmann manifold of 2-planes
| Autor: | Kazumi Tsukada |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Mathematics::Complex Variables Complex projective space 010102 general mathematics Mathematical analysis Structure (category theory) Kähler manifold 01 natural sciences Linear subspace Twistor theory Computational Theory and Mathematics Grassmannian 0103 physical sciences Cotangent bundle Twistor space Mathematics::Differential Geometry 010307 mathematical physics Geometry and Topology 0101 mathematics Mathematics::Symplectic Geometry Analysis Mathematics |
| Zdroj: | Differential Geometry and its Applications. 44:30-51 |
| ISSN: | 0926-2245 |
| DOI: | 10.1016/j.difgeo.2015.10.003 |
| Popis: | A complex Grassmann manifold G 2 ( C m + 2 ) of all 2-dimensional complex subspaces in C m + 2 has two nice geometric structures – the Kahler structure and the quaternionic Kahler structure. We study totally complex submanifolds of G 2 ( C m + 2 ) with respect to the quaternionic Kahler structure. We show that the projective cotangent bundle P ( T ⁎ C P m + 1 ) of a complex projective space C P m + 1 is a twistor space of the quaternionic Kahler manifold G 2 ( C m + 2 ) . Applying the twistor theory, we construct maximal totally complex submanifolds of G 2 ( C m + 2 ) from complex submanifolds of C P m + 1 . Then we obtain many interesting examples. In particular we classify maximal homogeneous totally complex submanifolds. We show the relationship between the geometry of complex submanifolds of C P m + 1 and that of totally complex submanifolds of G 2 ( C m + 2 ) . |
| Databáze: | OpenAIRE |
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