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On generalized $4$-th root metrics of isotropic scalar curvature

In: Mathematica Slovaca, vol. 68, no. 4
Akbar Tayebi
Detaily:
Rok, strany: 2018, 907 - 928
Kľúčové slová:
Akbar-Zadeh's scalar curvature, Bryant metric, Ricci curvature
O článku:
By an interesting physical perspective and a suitable contraction of the Riemannian curvature tensor in Finsler geometry, Akbar-Zadeh introduced the notion of scalar curvature for the Finsler metrics. A Finsler metric is called of isotropic scalar curvature if the scalar curvature depends on the position only. In this paper, we study the class of generalized $4$-th root metrics. These metrics generalize $4$-th root metrics which are used in Biology as ecological metrics. We find the necessary and sufficient condition under which a generalized $4$-th root metric is of isotropic scalar curvature. Then, we find the necessary and sufficient condition under which the conformal change of a generalized $4$-th root metric is of isotropic scalar curvature. Finally, we characterize the Bryant metrics of isotropic scalar curvature.
Ako citovať:
ISO 690:
Tayebi, A. 2018. On generalized $4$-th root metrics of isotropic scalar curvature. In Mathematica Slovaca, vol. 68, no.4, pp. 907-928. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0154

APA:
Tayebi, A. (2018). On generalized $4$-th root metrics of isotropic scalar curvature. Mathematica Slovaca, 68(4), 907-928. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0154
O vydaní:
Publikované: 10. 8. 2018