Natural Volume Forms on Pseudo-Finslerian Manifolds with $$m$$ th Root Metrics

IF 1.7 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2024-06-28 DOI:10.1134/s1061920824020146

A.V. Solov’yov

引用次数: 0

Abstract

We define natural volume forms on $n$-dimensional oriented pseudo-Finslerian manifolds with nondegenerate $m$-th root metrics. Our definitions of the natural volume forms depend on the parity of the positive integer $m>1$. The advantage of the stated definitions is their algebraic structure. The natural volume forms are expressed in terms of Cayley hyperdeterminants. In particular, the computation of the natural volume form does not require the difficult integration over the domain within the indicatrix in the tangent space $T_x M^n$ of the pseudo-Finslerian manifold at a point $x$.

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具有 $$m$$ th 根度量的伪芬斯勒方程上的自然体积形式

Abstract We define natural volume forms on $n$dimensional oriented pseudo-Finslerian manifolds with nondegenerate $m$-th root metrics.我们对自然体积形式的定义取决于正整数 $m>1$的奇偶性。所述定义的优势在于其代数结构。自然体积形式用 Cayley 超决定子表示。特别是，自然体积形式的计算不需要在点$x$处的伪芬斯勒流形的切空间$T_x M^n$的指示矩阵内的域上进行困难的积分。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.

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