Compact submanifolds of codimension p of a Sasakian space form
نویسندگان
چکیده
منابع مشابه
RICCI CURVATURE OF SUBMANIFOLDS OF A SASAKIAN SPACE FORM
Involving the Ricci curvature and the squared mean curvature, we obtain basic inequalities for different kind of submaniforlds of a Sasakian space form tangent to the structure vector field of the ambient manifold. Contrary to already known results, we find a different necessary and sufficient condition for the equality for Ricci curvature of C-totally real submanifolds of a Sasakian space form...
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Let $(M^{2n},g)$ be a real hypersurface with recurrent shapeoperator and tangent to the structure vector field $xi$ of the Sasakian space form$widetilde{M}(c)$. We show that if the shape operator $A$ of $M$ isrecurrent then it is parallel. Moreover, we show that $M$is locally a product of two constant $phi-$sectional curvaturespaces.
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It is proved that a Riemannian manifold M isometrically immersed in a Sasakian space form˜M(c) of constant ϕ-sectional curvature c < 1, with the structure vector field ξ tangent to M, satisfies Chen's basic equality if and only if it is a 3-dimensional minimal invariant submanifold. 1. Introduction. Let˜M be an m-dimensional almost contact manifold endowed with an almost contact structure (ϕ,ξ,...
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let $(m^{2n},g)$ be a real hypersurface with recurrent shapeoperator and tangent to the structure vector field $xi$ of the sasakian space form$widetilde{m}(c)$. we show that if the shape operator $a$ of $m$ isrecurrent then it is parallel. moreover, we show that $m$is locally a product of two constant $phi-$sectional curvaturespaces.
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ژورنال
عنوان ژورنال: Hokkaido Mathematical Journal
سال: 1985
ISSN: 0385-4035
DOI: 10.14492/hokmj/1381757645