Locally symmetric immersions

José Carmelo González-Dávila; Lieven Vanhecke

Czechoslovak Mathematical Journal (1999)

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

Abstract

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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.

How to cite

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González-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 -

References

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