Geometry of Mus-Gradient Metric

Year 2023, Volume: 5 Issue: 1, 1 - 10, 26.06.2023

Abderrahım Zagane

Abstract

In this paper, we give some properties of Riemannian curvature tensors of Mus-gradient metric .i.e. we characterize the Riemannian curvature, the sectional curvature, the Ricci tensor, the Ricci curvature and the scalar curvature.

Keywords

Riemannian manifold, Mus-gradient metric, Riemannian curvature

References

• Benkartab, A., & Cherif, A.M. (2019). New methods of construction for biharmonic maps. Kyungpook Math. J., 59(1), 135-147.
• Benkartab, A., & Cherif, A.M. (2020). Deformations of metrics and biharmonic maps. Commun. Math., 28(3), 263-275.
• Djaa, N. E., & Zagane, A. (2022). Harmonicity of deformed gradient metric. International Journal of Maps in Mathematics, 5(1), 61-77.
• Djaa, N. E., & Zagane, A. (2022). Some results on the geometry of a non-conformal deformation of a metric. Commun. Korean Math. Soc., 37(3), 865-879.
• Crasmareanu, M. (1999). Killing Potentials. An. Stiint. Univ. Al. I. Cuza Iasi. Mat.(NS), 45(1), 169-176.
• Djaa, N.E., Latti, F. & Zagane, A. (2022). Proper biharmonic maps on tangent bundle. arXiv preprint arXiv:2211.06661.
• Zagane, A. (2020). Geodesics on tangent bundles with horizontal Sasaki gradient metric. Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci., 40(4), 188-197.
• Zagane, A. (2021). Harmonic sections of tangent bundles with horizontal Sasaki gradient metric. Hagia Sophia Journal of Geometry, 3(2), 31-40.
• O’Neil, B. (1983). Semi-Riemannian geometry. Academic Press, New York.