Geometry of warped tangent bundles with Ricci-Flatness and shrinking solitions

Articles in Press

Document Type : Original Article

Authors

Department of Mathematics, Payame Noor University 19395-3697, Tehran, Iran

Abstract

‎In this paper‎, ‎we investigate the geometric structure of the tangent bundle of a warped product of two pseudo-Riemannian manifolds‎. ‎Let (M,g) and (M-,g-) be smooth pseudo-Riemannian manifolds‎, ‎and consider the‎‎warped product manifold (M×M-,g+e2fg-)‎, ‎where f is a smooth warping function‎. ‎We construct a Sasaki–Matsumoto type lift of the warped metric to define a pseudo-Riemannian metric on the tangent bundle‎, ‎which depends on a pair of smooth scalar functions and related to the total kinetic energy‎. We derive necessary and sufficient conditions under which the lifted metric on is Ricci-flat‎, ‎expressed in terms of the curvature properties of the base manifold and the structure functions‎. ‎Furthermore‎, ‎we prove that‎, ‎equipped with the metric‎, ‎admits a one-parameter family of shrinking Ricci solitons‎.

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References

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Journal of Finsler Geometry and its Applications

Articles in Press, Accepted Manuscript
Available Online from 19 August 2025

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