Formules de la moyenne, calcul de perturbations et théoremes d’annulation pour les formes harmoniques. (French) Zbl 0425.58022
MSC:
58J65 | Diffusion processes and stochastic analysis on manifolds |
60J60 | Diffusion processes |
60J57 | Multiplicative functionals and Markov processes |
58A12 | de Rham theory in global analysis |
58A14 | Hodge theory in global analysis |
Keywords:
stochastic parallel displacement; Hodge-deRham Laplacian; Weitzenbock formula; Feynman-Kac formula; vanishing theorem for 1-forms; smallest eigenvalue of the Ricci tensor; harmonic formsCitations:
Zbl 0241.60046References:
[1] | Bochner; Yano, Curvature and Betti Numbers (1953), Princeton University Press: Princeton University Press Princeton, NJ · Zbl 0051.39402 |
[2] | Darling; Siegert, (Proc. Nat. Acad.. Proc. Nat. Acad., Washington (1956)), 525 |
[3] | Eells; Elworthy, Stochastic Developpement, (Warwick Seminar (1970-1971)) · Zbl 0355.60053 |
[4] | J. Eells and P. Malliavin; J. Eells and P. Malliavin |
[5] | Ito, Stochastic parallel transport, (Internat. Congr. Math.. Internat. Congr. Math., Stockholm (1962)) |
[6] | Kac, M., (Second Symposium of Probability (1952), Univ. California: Univ. California Berkeley, CA) |
[7] | Malliavin, P., Géométrie Riemannienne stochastique, (Séminaire Jean Leray (1974), Collège de France) |
[8] | Morrow; Kodaira, Complex Manifolds (1971), New York · Zbl 0325.32001 |
[9] | Nijenhuis, Kon. Nederlandse Aka., 235 (1963) |
[10] | Pinsky, Trans. Amer. Math. Soc., 167, 89-113 (1972) |
[11] | de Rham, Variétés Différentiables (1956), Paris · Zbl 0065.32401 |
[12] | Stroock, Comm. Pure Appl. Math., 23, 447-457 (1970) · Zbl 0188.41103 |
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