Lagrange-Fedosov Nonholonomic Manifolds

Abstract

We outline an unified approach to geometrization of Lagrange mechanics, Finsler geometry and geometric methods of constructing exact solutions with generic off-diagonal terms and nonholonomic variables in gravity theories. Such geometries with induced almost symplectic structure are modelled on nonholonomic manifolds provided with nonintegrable distributions defining nonlinear connections. We introduce the concept of Lagrange-Fedosov spaces and Fedosov nonholonomic manifolds provided with almost symplectic connection adapted to the nonlinear connection structure. We investigate the main properties of generalized Fedosov nonholonomic manifolds and analyze exact solutions defining almost symplectic Einstein spaces.

latex2e, v3, published variant, with new S.V. affiliation

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Cited by in corpus (19)

• Principles of Einstein-Finsler Gravity and Perspectives in Modern Cosmology
• Finsler and Lagrange Geometries in Einstein and String Gravity
• Spectral Functionals, Nonholonomic Dirac Operators, and Noncommutative Ricci Flows
• Fedosov Quantization of Lagrange-Finsler and Hamilton-Cartan Spaces and Einstein Gravity Lifts on (Co) Tangent Bundles
• Deformation Quantization of Almost Kahler Models and Lagrange-Finsler Spaces
• Deformation Quantization of Nonholonomic Almost Kahler Models and Einstein Gravity
• Parametric Nonholonomic Frame Transforms and Exact Solutions in Gravity
• Einstein Gravity as a Nonholonomic Almost Kahler Geometry, Lagrange-Finsler Variables, and Deformation Quantization
• Clifford-Finsler Algebroids and Nonholonomic Einstein-Dirac Structures
• Curve Flows in Lagrange-Finsler Geometry, Bi-Hamiltonian Structures and Solitons
• Finsler-Lagrange Geometries and Standard Theories in Physics: New Methods in Einstein and String Gravity
• 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
• The Algebraic Index Theorem and Fedosov Quantization of Lagrange-Finsler and Einstein Spaces
• Nonholonomic Clifford Structures and Noncommutative Riemann--Finsler Geometry
• Nonholonomic Ricci Flows: I. Riemann Metrics and Lagrange-Finsler Geometry
• Nonholonomic Ricci Flows: Exact Solutions and Gravity
• On axiomatic formulation of gravity and matter field theories with MDRs and Finsler-Lagrange-Hamilton geometry on (co)tangent Lorentz bundles
• Nonholonomic Clifford and Finsler Structures, Non-Commutative Ricci Flows, and Mathematical Relativity