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Warped product semi-slant submanifolds in locally Riemannian product manifolds. (English) Zbl 1152.53022
In this paper, a class of submanifolds in locally Riemannian product manifold is studied. More precisely, the author deals with those warped product semi-slant submanifolds, that have warped product semi-invariant submanifolds and Riemannian product semi-slant submanifold. The paper provides the proof of the nonexistence of warped product proper semi-slant submanifolds with proper slant spheric submanifold. Additionally, by examples the existence of warped product semi-slant submanifolds with proper slant totally geodesic submanifold is proved.
MSC:
53C15Differential geometric structures on manifolds
53C40Global submanifolds (differential geometry)