Fractional Nonholonomic Ricci Flows

Abstract

We formulate the fractional Ricci flow theory for (pseudo) Riemannian geometries enabled with nonholonomic distributions defining fractional integro-differential structures, for non-integer dimensions. There are constructed fractional analogs of Perelman's functionals and derived the corresponding fractional evolution (Hamilton's) equations. We apply in fractional calculus the nonlinear connection formalism originally elaborated in Finsler geometry and generalizations and recently applied to classical and quantum gravity theories. There are also analyzed the fractional operators for the entropy and fundamental thermodynamic values.