Nonholonomic Ricci Flows of Riemannian Metrics and Lagrange-Finsler Geometry

A series of the most remarkable results in mathematics are related to Grisha Perelman’s proof of the Poincare Conjecture built on geometrization (Thurston) conjecture for three dimensional Riemannian manifolds, and R. Hamilton’s Ricciflow theory see reviews and basic references explained by Kleiner. Much of the works on Ricci flows has been performed and validated by experts in the area of geometrical analysis and Riemannian geometry. Recently, a number of applications in physics of the Ricci flow theory were proposed, by Vacaru. 

Some geometrical approaches in modern gravity and string theory are connected to the method of moving frames and distributions of geometric objects on (semi) Riemannian manifolds and their generalizations to spaces provided with nontrivial torsion, nonmetricity and/or nonlinear connection structures. Thegeometry of nonholonomic manifolds and non–Riemannian spaces is largely appliedin modern mechanics, gravity, cosmology and classical/quantum field theory expained by Stavrinos.