Symplectic reflections and complex space forms
Copyright policy )Symplectic reflections and complex space forms
Let (M,g,J) be a Hermitian manifold and N a submanifold of M. Then the reflection about N is called a symplectic reflection if it preserves the Kaehler form of (M,g,J). In this paper the authors prove the following Theorem. Let (M,g,J) be a Hermitian space of complex dimension \(n\geq 2\). Then it is a complex space form if and only if the local reflection with respect to any holomorphic surface is symplectic. This result generalizes Theorem 22 of [the authors, Geom. Dedicata 29, No.3, 259-277 (1989; Zbl 0673.53035)].
- Katholieke Universiteit Leuven Belgium
- Michigan State University United States
- KU Leuven Belgium
Local differential geometry of Hermitian and Kählerian structures, Global differential geometry of Hermitian and Kählerian manifolds, symplectic reflection, complex space form, Hermitian manifold
Local differential geometry of Hermitian and Kählerian structures, Global differential geometry of Hermitian and Kählerian manifolds, symplectic reflection, complex space form, Hermitian manifold
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