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Weakly symmetric spaces in complex and quaternionic space forms. (English) Zbl 0830.53041

We prove that some classes of generic submanifolds which include homogeneous real hypersurfaces in complex and quaternionic space forms are weakly symmetric spaces. In our method, the reflection with respect to a submanifold plays a central role.
Reviewer: S.Nagai (Saitama)

MSC:

53C30 Differential geometry of homogeneous manifolds
53B20 Local Riemannian geometry
53C40 Global submanifolds
53C55 Global differential geometry of Hermitian and Kählerian manifolds
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