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Pseudo-slant submanifolds of a Sasakian manifold. (English) Zbl 1117.53043
Let M ¯ be a Riemannian manifold equipped with an almost contact metric structure (ϕ,ξ,η,g). A submanifold M of M ¯ is said to be pseudo-slant if the structure vector field ξ is tangent to M everywhere, and if there exist two subbundles D 1 and D 2 of the tangent bundle TM of M such that TM decomposes orthogonally into TM=D 1 D 2 ξ, ϕD 1 is a subbundle of the normal bundle of M, and there exists a real number 0θ<π/2 such that for each nonzero vector XD 2 the angle between ϕX and D 2 is equal to θ. The authors derive some equations for certain tensor fields and investigate the integrability of some distributions on pseudo-slant submanifolds for the special case that the almost contact metric structure is Sasakian.
MSC:
53C40Global submanifolds (differential geometry)
53C25Special Riemannian manifolds (Einstein, Sasakian, etc.)