On \(\phi\)-recurrent generalized Sasakian-space-forms
The authors study \(\phi\)-recurrent generalized Sasakian-space-forms, i.e. almost contact metric manifolds satisfying additional conditions for the curvature tensor. In particular, the curvature tensor of such manifolds is of the form \[ \begin{multlined} R(X,Y)Z = f_1(g(Y,Z)X-g(X,Z)Y)+f_2(g(X,\phi Z)\phi Y-g(Y,\phi Z)\phi X+2 g(X,\phi Y)\phi Z)\\ +f_3(\eta(X)\eta(Z)Y-\eta(Y)\eta(Z)X+g(X,Z)\eta(Y)\xi-g(Y,Z)\eta(X)\xi)\end{multlined} \] for some functions \(f_1,f_2,f_3\). They obtain some results assuming that the dimension of the manifold is greater than \(3\) and that \(f_1-f_3\) is a non-zero constant.
scientific article; zbMATH DE number 6128345