Warped product submanifolds of cosymplectic manifolds. (English) Zbl 1161.53036

Warped product submanifolds were studied by R. L. Bishop and B. O’Neill [Trans. Am. Math. Soc. 145, 1–49 (1969; Zbl 0191.52002)]. It is well known that surfaces of revolution and Kenmotsu manifolds are warped product manifolds. B. Y. Chen studied \(CR\)-submanifolds of Kähler manifolds as warped product submanifolds [Monatsh. Math. 134, No. 2, 103–119 (2001; Zbl 0996.53045) and Monatsh. Math. 133, No. 3, 177–195 (2001; Zbl 0996.53044)]. B. Sahin [Geom. Dedicata 117, 195–202 (2006; Zbl 1093.53059)] and showed that there do not exist proper semi-slant warped product submanifolds of Kähler manifolds. As a generalization of warped product manifolds, doubly warped product manifolds were introduced by B. Ünal [Differ. Geom. Appl. 15, No. 3, 253–263 (2001; Zbl 1035.53100)].
In the paper under review, the authors study warped and doubly warped product manifolds, semi-slant warped product submanifolds and generic warped product submanifolds. They prove some results on the non-existence of such submanifolds in cosymplectic submanifolds.


53C40 Global submanifolds
53B25 Local submanifolds
Full Text: EuDML