On construit une nouvelle théorie de Hodge sur le fibré cotangent d’une variété Riemannienne . 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 et le flot géodésique sur .
We construct a new Hodge theory on the cotangent bundle of a Riemannian manifold . 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 and the geodesic flow on .
@article{SEDP_2003-2004____A21_0, author = {Bismut, Jean-Michel}, title = {Le {Laplacien} hypoelliptique}, journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"}, note = {talk:21}, publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique}, year = {2003-2004}, mrnumber = {2117053}, language = {fr}, url = {http://www.numdam.org/item/SEDP_2003-2004____A21_0/} }
TY - JOUR AU - Bismut, Jean-Michel TI - Le Laplacien hypoelliptique JO - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:21 PY - 2003-2004 DA - 2003-2004/// PB - Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://www.numdam.org/item/SEDP_2003-2004____A21_0/ UR - https://www.ams.org/mathscinet-getitem?mr=2117053 LA - fr ID - SEDP_2003-2004____A21_0 ER -
Bismut, Jean-Michel. Le Laplacien hypoelliptique. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2003-2004), Exposé no. 21, 15 p. http://www.numdam.org/item/SEDP_2003-2004____A21_0/
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