On LP-Kenmotsu Manifold with Regard to Generalized Symmetric Metric Connection of Type ( α, β )

Doddabhadrappla Gowda Prakasha (), Nasser Bin Turki, Mathad Veerabhadraswamy Deepika and İnan Ünal
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Doddabhadrappla Gowda Prakasha: Department of Mathematics, Davangere University, Shivagangothri, Davangere 577 007, India
Nasser Bin Turki: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Mathad Veerabhadraswamy Deepika: Department of Mathematics, Davangere University, Shivagangothri, Davangere 577 007, India
İnan Ünal: Department of Computer Engineering, Munzur University, Tunceli 62000, Turkey

Mathematics, 2024, vol. 12, issue 18, 1-17

Abstract: In the current article, we examine Lorentzian para-Kenmotsu (shortly, LP-Kenmotsu) manifolds with regard to the generalized symmetric metric connection ∇ G of type ( α , β ) . First, we obtain the expressions for curvature tensor, Ricci tensor and scalar curvature of an LP-Kenmotsu manifold with regard to the connection ∇ G . Next, we analyze LP-Kenmotsu manifolds equipped with the connection ∇ G that are locally symmetric, Ricci semi-symmetric, and φ -Ricci symmetric and also demonstrated that in all these situations the manifold is an Einstein one with regard to the connection ∇ G . Moreover, we obtain some conclusions about projectively flat, projectively semi-symmetric and φ -projectively flat LP-Kenmotsu manifolds concerning the connection ∇ G along with several consequences through corollaries. Ultimately, we provide a 5-dimensional LP-Kenmotsu manifold example to validate the derived expressions.

Keywords: Lorentzian para-Kenmotsu manifolds; generalized symmetric metric connection of type ( ? , ? ); Einstein manifold; projective curvature tensor (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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