Altunbaş, Murat

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.

Taşyurdu, Yasemin; Akpınar, Ayşe

In this study, we introduce new classes of octonion and sedenion numbers associated with Perrin numbers. We define Perrin octonions and Perrin sedenions by using the Perrin numbers. We give some relationship between Perrin octonions, Perrin sedenions and Perrin numbers. Moreover we obtain the generating functions, Binet formulas and sums formulas of them.