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Warped product pseudo-slant immersions in Sasakian manifolds. (English) Zbl 1399.53060

Summary: Recently, we have proved that there do not exist warped product semi-slant submanifolds of Sasakian manifolds other than contact CR-warped products which have been studied by I. Hasegawa and I. Mihai [Geom. Dedicata 102, 143–150 (2003; Zbl 1066.53103)]. In this paper, we introduce another class of submanifolds, called warped product pseudo-slant submanifolds. A characterization theorem for such immersions is obtained. Also, we establish an inequality for the squared norm of the second fundamental form in terms of the warping function and the slant angle. Furthermore, the equality case in the statement of the inequality is investigated, and we give two examples of pseudo-slant and warped product pseudo-slant submanifolds.

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C40 Global submanifolds
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53B25 Local submanifolds

Citations:

Zbl 1066.53103
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