# Locally symmetric immersions

José Carmelo González-Dávila; Lieven Vanhecke

Czechoslovak Mathematical Journal (1999)

- Volume: 49, Issue: 3, page 491-506
- ISSN: 0011-4642

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topGonzález-Dávila, José Carmelo, and Vanhecke, Lieven. "Locally symmetric immersions." Czechoslovak Mathematical Journal 49.3 (1999): 491-506. <http://eudml.org/doc/30501>.

@article{González1999,

abstract = {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.},

author = {González-Dávila, José Carmelo, Vanhecke, Lieven},

journal = {Czechoslovak Mathematical Journal},

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},

language = {eng},

number = {3},

pages = {491-506},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Locally symmetric immersions},

url = {http://eudml.org/doc/30501},

volume = {49},

year = {1999},

}

TY - JOUR

AU - González-Dávila, José Carmelo

AU - Vanhecke, Lieven

TI - Locally symmetric immersions

JO - Czechoslovak Mathematical Journal

PY - 1999

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 49

IS - 3

SP - 491

EP - 506

AB - 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.

LA - eng

KW - 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

UR - http://eudml.org/doc/30501

ER -

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