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Pseudo-slant submanifolds of a Sasakian manifold. (English) Zbl 1117.53043
Let $\overline{M}$ be a Riemannian manifold equipped with an almost contact metric structure $(\phi,\xi,\eta,g)$. A submanifold $M$ of $\overline{M}$ is said to be pseudo-slant if the structure vector field $\xi$ 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 $TM = D_1 \oplus D_2 \oplus {\Bbb R}\xi$, $\phi D_1$ is a subbundle of the normal bundle of $M$, and there exists a real number $0 \leq \theta < \pi/2$ such that for each nonzero vector $X \in D_2$ the angle between $\phi X$ and $D_2$ is equal to $\theta$. 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.

53C40Global submanifolds (differential geometry)
53C25Special Riemannian manifolds (Einstein, Sasakian, etc.)