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Keywords:
reflections; (locally) symmetric immersions; extrinsic (locally) symmetric submanifolds; parallel immersions; (locally) symmetric spaces
reflections; (locally) symmetric immersions; extrinsic (locally) symmetric submanifolds; parallel immersions; (locally) symmetric spaces
Summary:
We use reflections with respect to submanifolds and related geometric results to develop, inspired by the work of Ferus and other authors, in a unified way a local theory of extrinsic symmetric immersions and submanifolds in a general analytic Riemannian manifold and in locally symmetric spaces. In particular we treat the case of real and complex space forms and study additional relations with holomorphic and symplectic reflections when the ambient space is almost Hermitian. The global case is also taken into consideration and several examples are given.
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