## Formules de Lichnerowicz et théorème de l’indice. (Lichnerowicz formulas and index theorem.).(French)Zbl 0648.58033

Géométrie différentielle, Colloq. Géom. Phys., Paris/Fr. 1986, Trav. Cours 33, 11-31 (1988).
[For the entire collection see Zbl 0635.00010.]
In the first section of this paper the index theorem of M. F. Atiyah and I. M. Singer is proved by using probabilistic methods and Lichnerowicz formulas. In the second section the index theorem for families is proved by using localization formulas, superconnections of Levi-Civita-Quillen and $$\eta$$-invariant.
Reviewer: V.Deundjak

### MSC:

 58J20 Index theory and related fixed-point theorems on manifolds 60J65 Brownian motion 58J65 Diffusion processes and stochastic analysis on manifolds

Zbl 0635.00010