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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
To validate our findings, we construct a nontrivial example of a $3$-dimensional Riemannian manifold equipped with a semisymmetric nonmetric connection.
📌 3 Key Takeaways
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Objective & Hypothesis:We define a new type of semisymmetric nonmetric connection on a Riemannian manifold and establish its existence.
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Key Findings & Data:It is proved that such connection on a Riemannian manifold is projectively invariant under certain conditions.
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Conclusion & Impact:To validate our findings, we construct a nontrivial example of a $3$-dimensional Riemannian manifold equipped with a semisymmetric nonmetric connection.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Riemannian manifold · semisymmetric nonmetric connection · different curvature tensors
Abstract
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.
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Cite This Article
CHAUBEY, S. K., YILDIZ, A. (2019). Riemannian manifolds admitting a new type of semisymmetric nonmetric connection. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 4, 1887–1904. https://ajindex.com/articles/208976