Self-dual geometry of generalized Hermitian surfaces
- Moscow State Pedagogical University, Moscow (Russian Federation)
Several results on the geometry of conformally semiflat Hermitian surfaces of both classical and hyperbolic types (generalized Hermitian surfaces) are obtained. Some of these results are generalizations and clarifications of already known results in this direction due to Koda, Itoh, and other authors. They reveal some unexpected beautiful connections between such classical characteristics of conformally semiflat (generalized) Hermitian surfaces as the Einstein property, the constancy of the holomorphic sectional curvature, and so on. A complete classification of compact self-dual Hermitian RK-surfaces that are at the same time generalized Hopf manifolds is obtained. This provides a complete solution of the Chen problem in this class of Hermitian surfaces.
- OSTI ID:
- 21202763
- Journal Information:
- Sbornik. Mathematics, Vol. 189, Issue 1; Other Information: DOI: 10.1070/SM1998v189n01ABEH000288; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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