Soient M une variété Riemannienne compacte, E un fibré vectoriel Riemannien sur M et Σ le sous-fibré unitaire de E. On détermine des plongements de Σ dans E dont on prescrit des courbures de Gauss de divers types.
Let M be a compact Riemannian manifold, E a Riemannian vector bundle on M and Σ the sphere subbundle of E. We look for embeddings of Σ into E admitting prescribed Gaussian curvatures of various types.
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@article{CRMATH_2002__335_11_927_0,
author = {Hanani, Abdellah},
title = {Hypersurfaces d'un fibr\'e vectoriel {Riemannien} \`a courbure de {Gauss} prescrite},
journal = {Comptes Rendus. Math\'ematique},
pages = {927--930},
publisher = {Elsevier},
volume = {335},
number = {11},
year = {2002},
doi = {10.1016/S1631-073X(02)02588-8},
language = {fr},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02588-8/}
}
TY - JOUR AU - Hanani, Abdellah TI - Hypersurfaces d'un fibré vectoriel Riemannien à courbure de Gauss prescrite JO - Comptes Rendus. Mathématique PY - 2002 SP - 927 EP - 930 VL - 335 IS - 11 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(02)02588-8/ DO - 10.1016/S1631-073X(02)02588-8 LA - fr ID - CRMATH_2002__335_11_927_0 ER -
%0 Journal Article %A Hanani, Abdellah %T Hypersurfaces d'un fibré vectoriel Riemannien à courbure de Gauss prescrite %J Comptes Rendus. Mathématique %D 2002 %P 927-930 %V 335 %N 11 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(02)02588-8/ %R 10.1016/S1631-073X(02)02588-8 %G fr %F CRMATH_2002__335_11_927_0
Hanani, Abdellah. Hypersurfaces d'un fibré vectoriel Riemannien à courbure de Gauss prescrite. Comptes Rendus. Mathématique, Tome 335 (2002) no. 11, pp. 927-930. doi : 10.1016/S1631-073X(02)02588-8. http://www.numdam.org/articles/10.1016/S1631-073X(02)02588-8/
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