Reeb Flow Invariant Unit Tangent Sphere Bundles with the Kaluza-Klein Metric

Let (M,g) be an n−dimensional Riemannian manifold and T1M its tangent sphere bundle with the contact metric structure (G,η,φ,ξ), where G is the Kaluza-Klein metric. Let h =1/2Lξ φ be the structural operator and l =R(·,ξ)ξ be the characteristic Jacobi operator on T1M. In this paper, we find some conditions for the Reeb flow invariancy of the (0,2)− type tensors L and H defined by L(X,Ỹ) = g(lX,Ỹ) and H(X,Ỹ) = g(hX,Ỹ) for all vector fields X and Ỹ on T1M. © 2024, Prof. Dr. Mehmet Zeki SARIKAYA. All rights reserved.