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2012•Abstract and Applied AnalysisOpen access

A Classification of a Totally Umbilical SlantSubmanifold of Cosymplectic Manifolds

Siraj Uddin, Cenap Özel, Viqar Azam Khan

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Abstract

We study slant submanifolds of a cosymplectic manifold. It is shown that a totally umbilical slant submanifold M of a cosymplectic manifold 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.

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We study slant submanifolds of a cosymplectic manifold. It is shown that a totally umbilical slant submanifold M of a cosymplectic manifold 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.

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Available abstract

We study slant submanifolds of a cosymplectic manifold. It is shown that a totally umbilical slant submanifold M of a cosymplectic manifold 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.

Key concepts: Submanifold, Mathematics, Manifold (fluid mechanics), Geodesic, Totally geodesic, Invariant (physics), Pure mathematics, Mathematical analysis

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