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Structure Connection in an Almost Contact Metric Manifold

Bhavesh Sinha, S. L. Yadava

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Abstract

In 1970, semisymetric connection were studied by Yano [1] in a Riemannian manifold and in 1972 Mishra [2] studied affine connection in an almost contact Riemannian manifold. In the present paper we have defined a structure connnection in a Riemannian manifold and studied its properties in an almost contact metric manifold. It is seen that structure connection play fundamental role in an almost contact metric manifold.

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What this paper is about

In 1970, semisymetric connection were studied by Yano [1] in a Riemannian manifold and in 1972 Mishra [2] studied affine connection in an almost contact Riemannian manifold. In the present paper we have defined a structure connnection in a Riemannian manifold and studied its properties in an almost contact metric manifold. It is seen that structure connection play fundamental role in an almost contact metric manifold.

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Available abstract

In 1970, semisymetric connection were studied by Yano [1] in a Riemannian manifold and in 1972 Mishra [2] studied affine connection in an almost contact Riemannian manifold. In the present paper we have defined a structure connnection in a Riemannian manifold and studied its properties in an almost contact metric manifold. It is seen that structure connection play fundamental role in an almost contact metric manifold.

Key concepts: Levi-Civita connection, Connection (principal bundle), Statistical manifold, Fundamental theorem of Riemannian geometry, Pseudo-Riemannian manifold, Metric connection, Manifold (fluid mechanics), Metric (unit)

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