Geodesic
Locally symmetric immersions
Czechoslovak Mathematical Journal, Tome 49 (1999) no. 3, pp. 491-506 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 53B25, 53C35, 53C40, 53C42
Keywords: reflections; (locally) symmetric immersions; extrinsic (locally) symmetric submanifolds; parallel immersions; (locally) symmetric spaces 
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González-Dávila, J. C.; Vanhecke, L. Locally symmetric immersions. Czechoslovak Mathematical Journal, Tome 49 (1999) no. 3, pp. 491-506. http://geodesic.mathdoc.fr/item/CMJ_1999_49_3_a3/

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