WEAKLY STRETCH 4-DIMENSIONAL FINSLER MANIFOLDS

Document Type : Original Article

Author
Akbar Tayebi
Department of Mathematics, Faculty of Science, University of Qom, Qom. Iran
10.22034/maco.5.2.1
Abstract
There are some interesting Riemannian and non-Riemannian curvature in Riemann-Finsler geometry. Recently, the author introduced a new non-Riemannian quantity named mean stretch curvature. Taking trace with respect to fundamental tensor in first and second variables of stretch curvature gives rise the mean stretch curvature. A Finsler metric is said to be weakly stretch metric if has vanishing mean stretch curvature. In this paper, we are going to study the mean stretch curvature of 4-dimensional Finsler manifolds. First, we find the necessary and sufficient condition under which a 4-dimensional Finsler manifold is weakly stretch. Then, we show that the main scalars of a weakly stretch metric satisfies some certain PDEs.

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[1] S. A. Abbas and L. Kozma, On new classes of stretch Finsler metrics, J. Finsler Geom. Appl. 3(1) (2022), 86-99.
[2] F. Barati, On class of square Finsler metrics, J. Finsler Geom. Appl. 4(2) (2023), 74-91.
[3] L. Berwald, Uber Parallel¨ubertragung in R¨aumen mit allgemeiner Massbestimmung ¨ , Jber. Deutsch. Math.- Verein., 34(1926), 213-220.
[4] M. Matsumoto, An improvment proof of Numata and Shibata’s theorem on Finsler spaces of scalar curvature, Publ. Math. Debrecen. 64(2004), 489-500.
[5] B. Najafi and A. Tayebi, Weakly stretch Finsler metrics, Publ. Math. Debrecen, 91(2017), 441-454.
[6] B. N. Prasad and G. Shanker, Conformal change of four-dimensional Finsler space, Bull. Cal. Math. Soc. 102(5) (2010), 423-432.
[7] C. Shibata, On the curvature Rhijk of Finsler spaces of scalar curvature, Tensor, N.S. 32(1978), 311-317.
[8] A. Tayebi and B. Najafi, On a class of homogeneous Finsler metrics, J. Geom. Phys. 140(2019), 265-270.
[9] A. Tayebi and H. Sadeghi, On a class of stretch metrics in Finsler geometry, Arabian Journal of Mathematics, 8(2019), 153-160.
[10] A. Tayebi and T. Tabatabaeifar, Douglas-Randers manifolds with vanishing stretch tensor, Publ. Math. Debrecen, No. 3-4 86(2015), 423-432.
Mathematical Analysis and Convex Optimization
Volume 5, Issue 2
December 2025