Warped product submanifolds of Kaehler manifolds with a slant factor. (Warped product submanifolds of Kähler manifolds with a slant factor.) (English) Zbl 1162.53040

Summary: Recently, we showed that there exist no warped product semi-slant submanifolds in Kähler manifolds. On the other hand, Carriazo introduced anti-slant submanifolds as a particular class of bi-slant submanifolds. In this paper, we study such submanifolds in detail and show that they are useful to define a new kind of warped product submanifolds of Kähler manifolds. In this direction, we obtain the existence of warped product hemi-slant (anti-slant) submanifolds with examples. We give a characterization theorem and establish an inequality for the squared norm of the second fundamental form in terms of the warping function for such submanifolds. The equality case is also considered.


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