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

Khan, Khalid Ali; Khan, Viqar Azam; Siraj-Uddin

Balkan J. Geom. Appl. 13, No. 1, 55-65 (2008).

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.

Reviewer: Kazim Ilarslan (Kirikkale)

MSC:

53C40	Global submanifolds
53B25	Local submanifolds

Keywords:

warped product; generic warped product; semi-slant submanifold; cosymplectic manifold

Citations:

Zbl 0191.52002; Zbl 0996.53045; Zbl 0996.53044; Zbl 1093.53059; Zbl 1035.53100