By Yuri Gliklikh
The 1st version of this e-book entitled research on Riemannian Manifolds and a few difficulties of Mathematical Physics used to be released by means of Voronezh Univer sity Press in 1989. For its English variation, the booklet has been considerably revised and improved. particularly, new fabric has been extra to Sections 19 and 20. i'm thankful to Viktor L. Ginzburg for his labor at the transla tion and for writing Appendix F, and to Tomasz Zastawniak for his quite a few feedback. My designated thank you visit the referee for his helpful feedback at the concept of stochastic approaches. ultimately, i need to recognize the help of the AMS fSU relief Fund and the overseas technological know-how starting place (Grant NZBOOO), which made attainable my paintings on the various new effects integrated within the English version of the publication. Voronezh, Russia Yuri Gliklikh September, 1995 Preface to the Russian variation the current ebook is seemingly the 1st in monographic literature within which a typical remedy is given to 3 parts of worldwide research formerly consid ered fairly far away from one another, specifically, differential geometry and classical mechanics, stochastic differential geometry and statistical and quantum me chanics, and infinite-dimensional differential geometry of teams of diffeomor phisms and hydrodynamics. The unification of those themes below the canopy of 1 e-book appears to be like, although, fairly average, because the exposition relies on a geometrically invariant type of the Newton equation and its analogs taken as a primary legislations of movement.
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