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Einstein Type Curvature Tensors and Einstein Type Tensors of Generalized Riemannian Space in the Eisenhart Sense

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Abstract

By using decomposition of curvature tensors of generalized Riemannian space in the Eisenhart sense, the Einstein type curvature tensors and Einstein type tensors of that space are determined and defined. All these tensors vanish if the corresponding Ricci tensors also vanish in the observed space. All these tensors are traceless tensors and their properties of symmetry and anti-symmetry were examined. We proved that the Einstein type curvature tensors of the second kind, of the fourth kind and of the fifth kind are algebraic curvature tensors. The Einstein type tensors of the second kind, of the fourth kind and of the fifth kind are symmetric tensors.

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Acknowledgements

The authors are thankful to anonymous reviewer for valuable comments and suggestions. This research was financially supported by projects of the Ministry of Education, Science and Technological Development of the Republic of Serbia (project no. 451-03-9/2021-14/200123 for Miroslav D. Maksimović and project no. 451-03-9/2021-14/200124 for Milan Lj. Zlatanović) and supported by Faculty of Sciences and Mathematics, University of Priština in Kosovska Mitrovica (internal-junior project IJ-0203).

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences and Mathematics, University of Priština in Kosovska Mitrovica, Kosovska Mitrovica, Serbia

    Miroslav D. Maksimović

  2. Department of Mathematics, Faculty of Sciences and Mathematics, University of Niš, Niš, Serbia

    Milan Lj. Zlatanović

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  1. Miroslav D. Maksimović
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  2. Milan Lj. Zlatanović
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Correspondence to Miroslav D. Maksimović.

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Maksimović, M.D., Zlatanović, M.L. Einstein Type Curvature Tensors and Einstein Type Tensors of Generalized Riemannian Space in the Eisenhart Sense. Mediterr. J. Math. 19, 217 (2022). https://doi.org/10.1007/s00009-022-02119-x

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  • DOI: https://doi.org/10.1007/s00009-022-02119-x

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