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A class of semibasic vector 1-forms on Finsler manifolds

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Abstract

In this paper, we define conservative semibasic vector \(1-\)forms on the tangent bundle of a Finsler manifold. Using these vector \(1-\)forms, we characterize conservative \(L-\)Ehresmann connections with respect to the energy function. Then we find a correspondence between torsion-free semibasic vector \(1-\)forms and the subset of vertical vector fields. Taking into account this correspondence, we construct a class of semisprays that generates the Ehresmann connections mentioned above.

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Acknowledgments

We are indebted to the anonymous referee for her/his useful suggestions.

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Authors and Affiliations

  1. Faculty of Science, Department of Mathematics, University of Qom, Qom, Iran

    Akbar Tayebi & Mansoor Barzegari

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  1. Akbar Tayebi
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  2. Mansoor Barzegari
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Correspondence to Mansoor Barzegari.

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Tayebi, A., Barzegari, M. A class of semibasic vector 1-forms on Finsler manifolds. Period Math Hung 69, 239–250 (2014). https://doi.org/10.1007/s10998-014-0053-0

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  • DOI: https://doi.org/10.1007/s10998-014-0053-0

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