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 = {Jean-Michel Bismut and Gilles Lebeau},
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},
}
Jean-Michel Bismut; Gilles Lebeau. Laplacien hypoelliptique et torsion analytique. Comptes Rendus. Mathématique, Volume 341 (2005) no. 2, pp. 113-118. doi : 10.1016/j.crma.2005.06.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.06.003/
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