Nonholonomic Ricci flows and running cosmological constant: I. 4d Taub-nut metrics

In this work we construct and analyze exact solutions describing Ricci flows and nonholonomic deformations of four-dimensional (4D) Taub-NUT space-times. It is outlined a new geometric technique of constructing Ricci flow solutions. Some conceptual issues on space times provided with generic off-diagonal metrics and associated nonlinear connection structures are analyzed. The limit from gravity/Ricci flow models with nontrivial torsion to configurations with the Levi-Civita connection is allowed in some specific physical circumstances by constraining the class of integral varieties for the Einstein and Ricci flow equations.