CR-submanifolds of a trans-Sasakian manifold.

*(English)*Zbl 0767.53036An almost contact metric manifold $M(\phi ,\xi ,\eta ,g)$ is called trans-Sasakian if

$$\left({\nabla}_{X}\phi \right)Y=\alpha \{g(X,Y)\xi -\eta \left(Y\right)X\}+\beta \{g(\phi X,Y)\xi -\eta \left(Y\right)\phi X\},$$

$\alpha $ and $\beta $ being certain functions on $M$ [*J. A. Oubina*, Publ. Math. 32, 187- 193 (1985; Zbl 0611.53032)]. In this paper, CR-submanifolds of such manifolds are investigated. The conditions under which the distributions required by such manifolds are integrable are stated. $D$-parallel normal sections as well as totally umbilical CR-submanifolds are also studied.

Reviewer: Z.Olszak (Wrocław)