1. Rigidity properties of holomorphic isometries into homogeneous K\'{a}hler manifolds
- Author
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Loi, A. and Mossa, R.
- Subjects
Mathematics - Differential Geometry ,Mathematics - Complex Variables ,53C55, 32Q15, 53C24, 53C42 - Abstract
We prove two rigidity results on holomorphic isometries into homogeneous K\"{a}hler manifolds. The first shows that a K\"{a}hler-Ricci soliton induced by the homogeneous metric of the K\"{a}hler product of a special flag manifold (i.e. a flag of classical type or integral type) with a bounded homogeneous domain is trivial, i.e. K\"{a}hler-Einstein. In the second one we prove that: (i) a flat space is not relative to the K\"{a}hler product of a special flag manifold with a homogeneous bounded domain, (ii) a special flag manifold is not relative to the K\"{a}hler product of a flat space with a homogeneous bounded domain and (iii) a homogeneous bounded domain is not relative to the K\"{a}hler product of a flat space with a special flag manifold. Our theorems strongly extend the results in [4], [5], [12], [13] and [22]., Comment: 14 pages
- Published
- 2023
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