Quarter-Symmetric Non-Metric Connection of Non-Integrable Distributions

In this paper, we focus on non-integrable distributions with a quarter-symmetric non-metric connection (QSNMC) in generalized Riemannian manifold. First, by studying a quarter-symmetric connection on the generalized Riemannian manifold, we obtain the condition that the connection is non-metric. Then...

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Veröffentlicht in:Symmetry (Basel) 2024-07, Vol.16 (7), p.848
Hauptverfasser: Chen, Shuo, Liu, Haiming
Format: Artikel
Sprache:eng
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Zusammenfassung:In this paper, we focus on non-integrable distributions with a quarter-symmetric non-metric connection (QSNMC) in generalized Riemannian manifold. First, by studying a quarter-symmetric connection on the generalized Riemannian manifold, we obtain the condition that the connection is non-metric. Then, the Gauss, Codazzi and Ricci equations are proved for non-integrable distributions with respect to a quarter-symmetric non-metric connection in generalized Riemannian manifold. Furthermore, we deduce Chen’s inequalities for non-integrable distributions of real space forms with a quarter-symmetric non-metric connection in generalized Riemannian manifold as applications. After that, we give some examples of non-integrable distributions in Riemannian manifold with quarter-symmetric non-metric connection.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym16070848