Homotopy and Homology Vanishing Theorems and the Stability of Stochastic Flows

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We relate stability properties (i.e. moment exponents) of a stochastic dynamical system on a compact manifold $M$ to the homotopy and integral homology groups of $M$. In the special case of gradient Brownian systems associated to isometric immersions of $M$ in Euclidean space, these moment exponents can be estimated in terms of the second fundamental form of the immersion. This yields topological obstructions to isometric immersions generalizing results of Lawson-Simons and others. Our work also places these authors' work into the general framework of Weitzenböck formulas.
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Differential Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/152042

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/dg-ga/9503008
 http://arxiv.org/abs/dg-ga/9503008

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arXiv