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

We define natural volume forms on -dimensional oriented pseudo-Finslerian manifolds with nondegenerate -th root metrics. Our definitions of the natural volume forms depend on the parity of the positive integer . The advantage of the stated definitions is their algebraic structure. The natural volume...

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Bibliographic Details
Published inRussian journal of mathematical physics Vol. 31; no. 2; pp. 317 - 324
Main Author Solov’yov, A.V.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 2024
Springer Nature B.V
Subjects
14/34
639/766/189
639/766/530
639/766/747
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
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Summary:We define natural volume forms on -dimensional oriented pseudo-Finslerian manifolds with nondegenerate -th root metrics. Our definitions of the natural volume forms depend on the parity of the positive integer . 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 of the pseudo-Finslerian manifold at a point .
ISSN:1061-9208
1555-6638
DOI:10.1134/S1061920824020146