SPACE, TIME AND FUNDAMENTAL INTERACTIONS

Russian scientific journal

ISSN 2226-8812
Prostranstvo, vrema i fundamental’nye vzaimodejstvia
Parallel title: Space, time and fundamental interactions

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2025, no. 1

Invariant integration on pseudo-Finslerian manifolds

Solov'yov A.V.

We consider \(n\)-dimensional oriented pseudo-Finslerian manifolds with \(m\)th root metrics. Natural volume forms on these manifolds are defined. The natural volume forms depend on the parity of the positive integer \(m>1\) and are expressed in terms of Cayley hyperdeterminants. With the help of the introduced natural volume forms, we define invariant integrals of finite functions over \(n\)-dimensional oriented pseudo-Finslerian manifolds with \(m\)th root metrics.

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Keywords: volume forms, pseudo-Finslerian manifolds, \(m\)th root metrics, Cayley hyperdeterminants

UDC: 514.824, 514.763.62

PACS: 04.50.+h, 02.30.Cj

DOI: 10.17238/issn2226-8812.2025.1.150-153

Please cite this article in English as:
Solov’yov A. V. Invariant integration on pseudo-Finslerian manifolds. Space, Time and Fundamental Interactions, 2025, no. 1, pp. 150–153.