Le Laplacien hypoelliptique
Séminaire Équations aux dérivées partielles (Polytechnique) (2003-2004), Talk no. 21, 15 p.

We construct a new Hodge theory on the cotangent bundle of a Riemannian manifold X. The corresponding Laplacian is a second order hypoelliptic operator, which is self-adjoint with respect to a Hermitian form whose signature is ,. This Hodge theory interpolates between the classical Hodge theory on X and the geodesic flow on T*X.

On construit une nouvelle théorie de Hodge sur le fibré cotangent d’une variété Riemannienne X. Le Laplacien correspondant est un opérateur hypoelliptique d’ordre deux, qui est autoadjoint relativement à une forme Hermitienne de signature (,). Cette théorie de Hodge interpole entre la théorie de Hodge habituelle sur X et le flot géodésique sur T*X.

@article{SEDP_2003-2004____A21_0,
     author = {Bismut, Jean-Michel},
     title = {Le Laplacien hypoelliptique},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique)},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2003-2004},
     note = {talk:21},
     mrnumber = {2117053},
     language = {fr},
     url = {http://www.numdam.org/item/SEDP_2003-2004____A21_0}
}
Bismut, Jean-Michel. Le Laplacien hypoelliptique. Séminaire Équations aux dérivées partielles (Polytechnique) (2003-2004), Talk no. 21, 15 p. http://www.numdam.org/item/SEDP_2003-2004____A21_0/

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