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Uddin, Siraj; Ozel, Cenap; Khan, Viqar Azam

A classification of a totally umbilical slant submanifold of cosymplectic manifolds. (English) Zbl 1237.53023

Abstr. Appl. Anal. 2012, Article ID 716967, 8 p. (2012).
Summary: We study slant submanifolds of a cosymplectic manifold. It is shown that a totally umbilical slant submanifold \(M\) of a cosymplectic manifold \(\overline{M}\) is either an anti-invariant submanifold or a 1-dimensional submanifold. We show that every totally umbilical proper slant submanifold of a cosymplectic manifold is totally geodesic.

Cited in 3 Documents

MSC:

53B25 Local submanifolds
53D05 Symplectic manifolds (general theory)
53D10 Contact manifolds (general theory)

Keywords:

cosymplectic manifold; umbilical slant submanifold
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References:

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