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Riemannian manifolds admitting a new type of semisymmetric nonmetric connection. (English) Zbl 1433.53026

Summary: We define a new type of semisymmetric nonmetric connection on a Riemannian manifold and establish its existence. It is proved that such connection on a Riemannian manifold is projectively invariant under certain conditions. We also find many basic results of the Riemannian manifolds and study the properties of group manifolds and submanifolds of the Riemannian manifolds with respect to the semisymmetric nonmetric connection. To validate our findings, we construct a nontrivial example of a 3-dimensional Riemannian manifold equipped with a semisymmetric nonmetric connection.

MSC:

53B20 Local Riemannian geometry
53B05 Linear and affine connections
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References:

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