Semi-slant submanifolds of a Sasakian manifold
type: Item
instance of: scholarly article
title: Semi-slant submanifolds of a Sasakian manifold
zbMATH Open document ID: 0944.53028
DOI: 10.1023/A:1005241320631
author: Yanyan Li
published in: Geometriae Dedicata
publication date: 2000-09-12T00:00:00Z
review text: Let \(\widetilde M\) be an almost contact metric manifold and \((\varphi,\xi,\eta,g)\) its almost contact metric structure [see, e.g., \textit{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 \(\mathcal D\) 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 \(\mathcal D_p\). The submanifold (the distribution \(\mathcal D\)) is said to be slant [\textit{A. Lotta}, Bull. Math. Soc. Roum. 39, 183-198 (1996; Zbl 0885.53058)] if the angle \(\theta(X)\) is independent of the choice of \(X\in\mathcal D_p\) and \(p\in M\). The authors define \(M\) to be semi-slant if there exist two orthogonal distributions \(\mathcal D_1\), \(\mathcal D_2\) such that \(TM=\mathcal D_1\oplus\mathcal D_2\oplus\{\xi\}\), \(\mathcal D_1\) is invariant (\(\varphi(\mathcal D_1)=\mathcal D_1\)) and \(\mathcal D_2\) 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.
reviewed by: Zbigniew Olszak
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53D15
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 1384071
zbMATH Keywords: almost contact metric manifold
zbMATH Keywords: Sasakian manifold
zbMATH Keywords: slant submanifold
zbMATH Keywords: semi-slant submanifold
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1384071