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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Furthermore, we define sectional curvatures of $WS(g,w,\pi,\mu)$ and prove that any isotropic Weyl manifold $WS(g,w,\pi,\mu)$ is locally conformal to an Einstein manifold with a semisymmetric recurrent-metric connection, $EWS(g,w,\pi,\mu)$.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, Weyl manifolds, denoted by $WS(g,w,\pi,\mu)$, having a special a semisymmetric recurrent-metric connection are introduced and the uniqueness of this connection is proved.
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Key Findings & Data:We give an example of $WS(g,w,\pi,\mu)$ with a constant scalar curvature.
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Conclusion & Impact:Furthermore, we define sectional curvatures of $WS(g,w,\pi,\mu)$ and prove that any isotropic Weyl manifold $WS(g,w,\pi,\mu)$ is locally conformal to an Einstein manifold with a semisymmetric recurrent-metric connection, $EWS(g,w,\pi,\mu)$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Weyl manifold · semisymmetric connection · recurrent-metric connection
Abstract
In this paper, Weyl manifolds, denoted by $WS(g,w,\pi,\mu)$, having a special a semisymmetric recurrent-metric connection are introduced and the uniqueness of this connection is proved. We give an example of $WS(g,w,\pi,\mu)$ with a constant scalar curvature. Furthermore, we define sectional curvatures of $WS(g,w,\pi,\mu)$ and prove that any isotropic Weyl manifold $WS(g,w,\pi,\mu)$ is locally conformal to an Einstein manifold with a semisymmetric recurrent-metric connection, $EWS(g,w,\pi,\mu)$.
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Cite This Article
ÖZDEMİR, F., TÜRKOĞLU, M. D. (2019). Sectional curvatures on Weyl manifolds with a special metric connection. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 1, 224–240. https://ajindex.com/articles/214998