Cartan Connections for Stochastic Developments on sub-Riemannian Manifolds
نویسندگان
چکیده
Analogous to the characterisation of Brownian motion on a Riemannian manifold as development Euclidean space, we construct sub-Riemannian diffusions equinilpotentisable manifolds by developing canonical stochastic process arising lift an associated model space. The notion introduce for uses Cartan connections, which take place Levi-Civita connection in geometry. We first derive general expression generator is with respect further provide necessary and sufficient condition existence develops diffusion sub-Laplacian defined Popp’s volume. illustrate construction suitable free structures two generators discuss example where not satisfied.
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ژورنال
عنوان ژورنال: Journal of Geometric Analysis
سال: 2021
ISSN: ['1559-002X', '1050-6926']
DOI: https://doi.org/10.1007/s12220-021-00743-9