Ricci Flows and Solitonic pp--Waves

Abstract

We find exact solutions describing Ricci flows of four dimensional pp-waves nonlinearly deformed by two/three dimensional solitons. Such solutions are parametrized by five dimensional metrics with generic off-diagonal terms and connections with nontrivial torsion which can be related, for instance, to antisymmetric tensor sources in string gravity. There are defined nontrivial limits to four dimensional configurations and the Einstein gravity.

The variant accepted to IJMPA, with new affiliation, 16 pages

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• On General Solutions for Field Equations in Einstein and Higher Dimension Gravity
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• The Entropy of Lagrange-Finsler Spaces and Ricci Flows
• Curve Flows in Lagrange-Finsler Geometry, Bi-Hamiltonian Structures and Solitons
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• Geometric Flows and Perelman's Thermodynamics for Black Ellipsoids in $R^2$ and Einstein Gravity Theories
• On Supersymmetric Geometric Flows and ${\mathcal{R}}^2$ Inflation From Scale Invariant Supergravity
• Nonholonomic Ricci Flows and Running Cosmological Constant: I. 4D Taub-NUT Metrics
• Principles of Einstein-Finsler Gravity and Cosmology
• Black Holes, Ellipsoids, and Nonlinear Waves in Pseudo-Finsler Spaces and Einstein Gravity
• Metric Compatible or Noncompatible Finsler-Ricci Flows
• Quantum geometric information flows and relativistic generalizations of G. Perelman thermodynamics for nonholonomic Einstein systems with black holes and stationary solitonic hierarchies
• Nonholonomic Black Ring and Solitonic Solutions in Finsler and Extra Dimension Gravity Theories
• Off-diagonal cosmological solutions in emergent gravity theories and Grigory Perelman entropy for geometric flows
• General off-diagonal integrability of metric and nonmetric geometric flow and Finsler-Lagrange-Hamilton modified Einstein equations