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ON PROJECTIVELY RELATED WARPED PRODUCT FINSLER MANIFOLDS

M. M. REZAII

Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Ave., Tehran, Iran

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and

Y. ALIPOUR-FAKHRI

Department of Mathematical Science, Tabriz University, Tabriz, P. O. Box 5166616471, Iran

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https://doi.org/10.1142/S0219887811005464Cited by:1 (Source: Crossref)

Abstract

Let 𝔽₁ = (M₁,F₁) and 𝔽₂ = (M₂,F₂) be two Finsler manifolds and let M = M₁ × M₂ and S is a spray in M. Also 𝔽 = (M₁ × _f M₂, F) is a warped product Finsler manifolds, such that the function f : M₁ → ℝ₊ is not constant. In this paper, we define a non-linear connection on warped product 𝔽, and finally, we have presented some necessary and sufficient conditions under which the spray manifold (M₁ × M₂, S) is projectively equivalent to the warped product Finsler manifolds (M₁ × _f M₂, F).

Keywords:

AMSC: 53C60, 53D05, 58B20

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