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Zbl 0944.53028
Cabrerizo, J.L.; Carriazo, A.; Fernández, L.M.; Fernández, M.
Semi-slant submanifolds of a Sasakian manifold.
(English)
[J] Geom. Dedicata 78, No.2, 183-199 (1999). ISSN 0046-5755; ISSN 1572-9168/e

Let $\widetilde M$ be an almost contact metric manifold and $(\varphi,\xi,\eta,g)$ its almost contact metric structure [see, e.g., {\it D. E. Blair}, Lect. Notes Math. 509, Springer-Verlag (1976; Zbl 0319.53026)]. Let $M$ be a Riemannian manifold isometrically immersed in $\widetilde M$, for which the structure vector field $\xi$ is tangent to $M$. Denote by $\Cal D$ the orthogonal complement of $\xi$ in $TM$. For a nonzero vector $X\in T_pM$, which is not colinear with $\xi_p$, denote by $\theta(X)$ the angle between $\varphi X$ and $\Cal D_p$. The submanifold (the distribution $\Cal D$) is said to be slant [{\it A. Lotta}, Bull. Math. Soc. Roum. 39, 183-198 (1996; Zbl 0885.53058)] if the angle $\theta(X)$ is independent of the choice of $X\in\Cal D_p$ and $p\in M$. The authors define $M$ to be semi-slant if there exist two orthogonal distributions $\Cal D_1$, $\Cal D_2$ such that $TM=\Cal D_1\oplus\Cal D_2\oplus\{\xi\}$, $\Cal D_1$ is invariant ($\varphi(\Cal D_1)=\Cal D_1$) and $\Cal D_2$ is slant. They find necessary and sufficient conditions for $M$ to be semi-slant, and study properties of such submanifolds. Among other things, they study integrability conditions for various distributions involved with the definition of semi-slantness in the case when the ambient manifold is Sasakian. See also recent papers by the same authors.
[Z.Olszak (Wrocław)]
MSC 2000:
*53C40 Submanifolds (differential geometry)
53D15 Almost contact and almost symplectic manifolds
53C25 Special Riemannian manifolds

Keywords: almost contact metric manifold; Sasakian manifold; slant submanifold; semi-slant submanifold

Citations: Zbl 0319.53026; Zbl 0885.53058

Cited in: Zbl 1241.53037 Zbl 1172.53036

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