Nonholonomic Ricci Flows of Riemannian Metrics and Lagrange-Finsler Geometry

Abstract

In this paper, the theory of the Ricci flows for manifolds is elaborated with nonintegrable (nonholonomic) distributions defining nonlinear connection structures. Such manifolds provide a unified geometrical arena for nonholonomic Riemannian spaces, Lagrange mechanics, Finsler geometry, and various models of gravity (the Einstein theory and string, or gauge, generalizations). Nonhlonomic frames are considered with associated nonlinear connection structure and certain defined classes of nonholonomic constraints on Riemann manifolds for which various types of generalized Finsler geometries can be modelled by Ricci flows. We speculate upon possible applications of the nonholonomic flows in modern geometrical mechanics and physics.