Harmonie reflections
Lieven Vanhecke; Maria-Elena Vazquez-Abal
- Volume: 82, Issue: 2, page 229-236
- ISSN: 1120-6330
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topVanhecke, Lieven, and Vazquez-Abal, Maria-Elena. "Harmonie reflections." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 82.2 (1988): 229-236. <http://eudml.org/doc/287366>.
@article{Vanhecke1988,
abstract = {We study local reflections $\phi_\{\sigma\}$ with respect to a curve $\sigma$ in a Riemannian manifold and prove that $\sigma$ is a geodesic if $\phi_\{\sigma\}$ is a harmonic map. Moreover, we prove that the Riemannian manifold has constant curvature if and only if $\phi_\{\sigma\}$ is harmonic for all geodesies $\sigma$.},
author = {Vanhecke, Lieven, Vazquez-Abal, Maria-Elena},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Harmonic maps; Reflections with respect to a curve; Harmonic reflections; local reflection; harmonic map; geodesic; constant curvature},
language = {eng},
month = {6},
number = {2},
pages = {229-236},
publisher = {Accademia Nazionale dei Lincei},
title = {Harmonie reflections},
url = {http://eudml.org/doc/287366},
volume = {82},
year = {1988},
}
TY - JOUR
AU - Vanhecke, Lieven
AU - Vazquez-Abal, Maria-Elena
TI - Harmonie reflections
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1988/6//
PB - Accademia Nazionale dei Lincei
VL - 82
IS - 2
SP - 229
EP - 236
AB - We study local reflections $\phi_{\sigma}$ with respect to a curve $\sigma$ in a Riemannian manifold and prove that $\sigma$ is a geodesic if $\phi_{\sigma}$ is a harmonic map. Moreover, we prove that the Riemannian manifold has constant curvature if and only if $\phi_{\sigma}$ is harmonic for all geodesies $\sigma$.
LA - eng
KW - Harmonic maps; Reflections with respect to a curve; Harmonic reflections; local reflection; harmonic map; geodesic; constant curvature
UR - http://eudml.org/doc/287366
ER -
References
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- VANHECKE, L. and WILLMORE, T.J., Interaction of tubes ad spheres, «Math. Ann.» 263 (1983), 31-42. Zbl0491.53034MR697328DOI10.1007/BF01457081
- VANHECKE, L., Geometry and symmetry, Proc. Workshop on Advances in Differential Geometry and Topology, Torino1987, to appear. Zbl0766.53043
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