Factorization of diffusions on fibre bundles

Author:
Ming Liao

Journal:
Trans. Amer. Math. Soc. **311** (1989), 813-827

MSC:
Primary 58G32; Secondary 53C10

DOI:
https://doi.org/10.1090/S0002-9947-1989-0929666-4

MathSciNet review:
929666

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a fibre bundle with a -structure and a connection. A -invariant operator on the standard fibre is "shifted" to an operator on and a semielliptic operator on is "lifted" to an operator on . Let be an -diffusion on , let be a -diffusion on which is independent of and let be its horizontal lift in the associated principal bundle. Then is a diffusion on with generator . Conversely, such a factorization is possible only if the fibre bundle has a proper -structure. In the case of a Riemannian submersion, and can be taken to be Brownian motions and the existence of a -structure then means that the fibres are totally geodesic.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1989-0929666-4

Keywords:
Diffusions,
elliptic operators,
fibre bundles,
structure groups,
connections,
Riemannian submersions,
totally geodesic fibres

Article copyright:
© Copyright 1989
American Mathematical Society