相关论文: Nonlinear Connections and Spinor Geometry
This is the first monograph on the geometry of anisotropic spinor spaces and its applications in modern physics. The main subjects are the theory of gravity and matter fields in spaces provided with off--diagonal metrics and associated…
We generalize the geometry of Santilli's locally anisotropic and inhomogeneous isospaces to the geometry of vector isobundles provided with nonlinear and distinguished isoconnections and isometric structures. We present, apparently for the…
We generalize the geometry of Santilli's locally anisotropic and inhomogeneous isospaces to the geometry of vector isobundles provided with nonlinear and distinguished isoconnections and isometric structures. We present, apparently for the…
In this short pedagogical presentation, we introduce the spin groups and the spinors from the point of view of group theory. We also present, independently, the construction of the low dimensional Clifford algebras. And we establish the…
In this article, we review the current status of Finsler-Lagrange geometry and generalizations. The goal is to aid non-experts on Finsler spaces, but physicists and geometers skilled in general relativity and particle theories, to…
A continuum mechanical theory with foundations in generalized Finsler geometry describes the complex anisotropic behavior of skin. A fiber bundle approach, encompassing total spaces with assigned linear and nonlinear connections,…
We give an introduction to (pseudo-)Finsler geometry and its connections. For most results we provide short and self contained proofs. Our study of the Berwald non-linear connection is framed into the theory of connections over general…
We analyze the foundations of Finsler gravity theories with metric compatible connections constructed on nonholonomic tangent bundles, or (pseudo) Riemannian manifolds. There are considered "minimal" modifications of Einstein gravity…
We summarize the main results of our recent investigation of bundles of real Clifford modules and briefly touch on some applications to string theory and supergravity.
Finsler geometry is a natural generalization of (pseudo-)Riemannian geometry, where the line element is not the square root of a quadratic form but a more general homogeneous function. Parameterizing this in terms of symmetric tensors…
By bridging geometric and algebraic concepts, this dissertation lays the groundwork for a comprehensive study of the Clifford structures on bundles and spinor fields. We delve into the K\"ahler-Atiyah bundle, which encapsulates the essence…
The classification of emergent spinor fields according to modified bilinear covariants is scrutinized, in spacetimes with nontrivial topology, which induce inequivalent spin structures. Extended Clifford algebras, constructed by equipping…
Various types of Lagrange and Finsler geometries and the Einstein gravity theory, and modifications, can be modelled by nonholonomic distributions on tangent bundles/ manifolds when the fundamental geometric objects are adapted to nonlinear…
The monograph gives a general geometric background of the theory of field interactions, strings and diffusion processes on spaces, superspaces and isospaces with higher order anisotropy and inhomogenity. Our approach proceeds by developing…
In this review, basic definitions of spin geometry are given and some of its applications to supersymmetry, supergravity and condensed matter physics are summarized. Clifford algebras and spinors are defined and the first-order differential…
We apply the method of moving anholonomic frames, with associated nonlinear connections, in (pseudo) Riemannian spaces and examine the conditions when various types of locally anisotropic (la) structures (Lagrange, Finsler like and more…
We elaborate an unified geometric approach to classical mechanics, Riemann-Finsler spaces and gravity theories on Lie algebroids provided with nonlinear connection (N-connection) structure. There are investigated the conditions when the…
In this article, we review some aspects of gravitational field and cosmology based on Finsler and Finsler-like generalized metric structures. The geometrical framework of these spaces allows further investigation of locally-anisotropic…
This is a survey article on recent progress of comparison geometry and geometric analysis on Finsler manifolds of weighted Ricci curvature bounded below. Our purpose is two-fold: Give a concise and geometric review on the birth of weighted…
Classical anti-commuting spinor fields and their dynamics are derived from the geometry of the Clifford bundle over spacetime via the BRST formulation. In conjunction with Kaluza-Klein theory, this results in a geometric description of all…