Contact CR-warped product submanifolds in Sasakian manifolds. (English) Zbl 1066.53103

Hasegawa, Izumi; Mihai, Ion

Geom. Dedicata 102, 143-150 (2003).

Recently, B.-Y. Chen studied warped products which are CR-submanifolds in Kähler manifolds and established general sharp inequalities for CR-warped products in Kähler manifolds. In the present paper, we obtain a sharp inequality for the squared norm of the second fundamental form (an extrinsic invariant) in terms of the warping function for contact CR-warped products isometrically immersed in Sasakian manifolds. The equality case is considered. Also, the minimum codimension of a contact CR-warped product in an odd-dimensional sphere is determined.

Reviewer: Marcella Palese (Turin)

MSC:

53C40

Global submanifolds

Keywords:

contact CR-submanifold; Sasakian manifold; Sasakian space form; warped product