On explicite les propriétés d'analyse du Laplacien hypoelliptique sur le fibré cotangent d'une variété Riemannienne compacte X. On montre qu'il est effectivement une déformation du Laplacien ordinaire sur X. On relie la torsion analytique du Laplacien hypoelliptique à la torsion analytique de Ray–Singer du Laplacien sur X.
We establish analytical properties of the hypoelliptic Laplacian on the cotangent bundle of a Riemannian manifold. We show that it is, in the proper sense, a deformation of the classical Laplacian on X. We give a formula relating the analytic torsion of the hypoelliptic Laplacian to the Ray–Singer analytic torsion of the Laplacian of X.
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@article{CRMATH_2005__341_2_113_0,
author = {Bismut, Jean-Michel and Lebeau, Gilles},
title = {Laplacien hypoelliptique et torsion analytique},
journal = {Comptes Rendus. Math\'ematique},
pages = {113--118},
publisher = {Elsevier},
volume = {341},
number = {2},
year = {2005},
doi = {10.1016/j.crma.2005.06.003},
language = {fr},
url = {http://www.numdam.org/articles/10.1016/j.crma.2005.06.003/}
}
TY - JOUR AU - Bismut, Jean-Michel AU - Lebeau, Gilles TI - Laplacien hypoelliptique et torsion analytique JO - Comptes Rendus. Mathématique PY - 2005 SP - 113 EP - 118 VL - 341 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2005.06.003/ DO - 10.1016/j.crma.2005.06.003 LA - fr ID - CRMATH_2005__341_2_113_0 ER -
%0 Journal Article %A Bismut, Jean-Michel %A Lebeau, Gilles %T Laplacien hypoelliptique et torsion analytique %J Comptes Rendus. Mathématique %D 2005 %P 113-118 %V 341 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2005.06.003/ %R 10.1016/j.crma.2005.06.003 %G fr %F CRMATH_2005__341_2_113_0
Bismut, Jean-Michel; Lebeau, Gilles. Laplacien hypoelliptique et torsion analytique. Comptes Rendus. Mathématique, Tome 341 (2005) no. 2, pp. 113-118. doi : 10.1016/j.crma.2005.06.003. http://www.numdam.org/articles/10.1016/j.crma.2005.06.003/
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