Some classes of pseudosymmetric contact metric 3-manifolds (Q415746)

Pseudosymmetric manifolds are a natural generalization of semisymmetric manifolds first studied by E. Cartan:NEWLINENEWLINE A Riemannian manifold \((M^m,g)\), \(m\geq 3\), is called pseudosymmetric if at every point of \(M^m\) the curvature tensor satisfies the condition NEWLINE\[NEWLINE(R(X,Y)\cdot R)(X_1,X_2,X_3)= L\{(X\wedge Y)\cdot R(X_1,X_2,X_3)\}NEWLINE\]NEWLINE for any \(X,Y,X_1,X_2,X_3\in{\mathcal X}(M^m)\), and \(L\) is a smooth function.NEWLINENEWLINE The aim of the paper is to study some types of three-dimensional pseudosymmetric contact metric manifolds. In particular, three-dimensional \((\kappa,\mu,\nu)\)-contact metric pseudosymmetric manifolds of type constant in the direction of the structural vector \(\xi\) are considered.