We prove that the universal coveting spaces of the genetic submanifolds MCk,...,m0 of CP~ and Mhk ,...,r~o of CHn are naturally reductive homogeneous spaces by determining explicitly tensor fields defining naturally reductive homogeneous structures on them.
A class of submanifolds of homogeneous reductive spaces
β Scribed by V. I. Marmazeev
- Publisher
- SP MAIK Nauka/Interperiodica
- Year
- 1981
- Tongue
- English
- Weight
- 263 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0001-4346
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π SIMILAR VOLUMES
Let K be a compact connected Lie group, L be a closed subgroup of K. It is well known that L is a subgroup of maximal rank of K if and only if the Euler characteristic of the manifold K/L is positive. The homotopy classification of such homogeneous spaces KIL in case L is connected was obtained in .
Let K be a compact connected Lie group, L be a connected closed subgroup of K. It is well known that L is a subgroup of maximal rank of K if and only if the Euler characteristic of the manifold M = K/L is positive. Such homogeneous spaces M have been classified in [7,10]. However, their topological