Nonholonomic Clifford and Finsler Structures, Non-Commutative Ricci Flows, and Mathematical Relativity

Abstract

In this summary of Habilitation Thesis, it is outlined author's 18 years research activity on mathematical physics, geometric methods in particle physics and gravity, modifications and applications (after defending his PhD thesis in 1994). Ten most relevant publications are structured conventionally into three "strategic directions": 1) nonholonomic geometric flows evolutions and exact solutions for Ricci solitons and field equations in (modified) gravity theories; 2) geometric methods in quantization of models with nonlinear dynamics and anisotropic field interactions; 3) (non) commutative geometry, almost Kaehler and Clifford structures, Dirac operators and effective Lagrange-Hamilton and Riemann-Finsler spaces.

arXiv commentlatex 2e, 11pt, 129 pages; the review is performed following a Guide on Habilitation Theses, see http://www.cnatdcu.ro/wp-content/uploads/2011/11/Ghid-de-abilitare-2012.pdf

References in corpus (26)

• Principles of Einstein-Finsler Gravity and Perspectives in Modern Cosmology
• Spectral Functionals, Nonholonomic Dirac Operators, and Noncommutative Ricci Flows
• Spinors in Higher Dimensional and Locally Anisotropic Spaces
• Anholonomic Soliton-Dilaton and Black Hole Solutions in General Relativity
• Ellipsoidal, Cylindrical, Bipolar and Toroidal Wormholes in 5D Gravity
• Finsler Black Holes Induced by Noncommutative Anholonomic Distributions in Einstein Gravity
• Fedosov Quantization of Lagrange-Finsler and Hamilton-Cartan Spaces and Einstein Gravity Lifts on (Co) Tangent Bundles
• Critical Remarks on Finsler Modifications of Gravity and Cosmology by Zhe Chang and Xin Li
• Einstein Gravity as a Nonholonomic Almost Kahler Geometry, Lagrange-Finsler Variables, and Deformation Quantization
• Interactions, Strings and Isotopies in Higher Order Anisotropic Superspaces
• Clifford-Finsler Algebroids and Nonholonomic Einstein-Dirac Structures
• Locally Anisotropic Wormholes and Flux Tubes in 5D Gravity
• Lagrange-Fedosov Nonholonomic Manifolds
• The Entropy of Lagrange-Finsler Spaces and Ricci Flows
• Constant Curvature Coefficients and Exact Solutions in Fractional Gravity and Geometric Mechanics
• New Classes of Off-Diagonal Cosmological Solutions in Einstein Gravity
• Einstein Gravity in Almost Kahler Variables and Stability of Gravity with Nonholonomic Distributions and Nonsymmetric Metrics
• Generalized Lagrange Transforms: Finsler Geometry Methods and Deformation Quantization of Gravity
• Loop Quantum Gravity in Ashtekar and Lagrange-Finsler Variables and Fedosov Quantization of General Relativity
• Nonholonomic Ricci Flows and Parametric Deformations of the Solitonic pp--Waves and Schwarzschild Solutions
• Stochastic Processes and Thermodynamics on Curved Spaces
• Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics
• Nonholonomic Ricci Flows: Exact Solutions and Gravity
• Fractional Analogous Models in Mechanics and Gravity Theories
• Nonholonomic Black Ring and Solitonic Solutions in Finsler and Extra Dimension Gravity Theories
• Fractional Exact Solutions and Solitons in Gravity