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.

latex 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 (7)

• 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 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
• Nonholonomic Ricci Flows and Parametric Deformations of the Solitonic pp--Waves and Schwarzschild Solutions
• Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics
• Nonholonomic Ricci Flows: Exact Solutions and Gravity