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REMARKS ON METALLIC MAPS BETWEEN METALLIC RIEMANNIAN MANIFOLDS AND CONSTANCY OF CERTAIN MAPS
Akyol, Mehmet Akif The Honam Mathematical Society 2019 호남수학학술지 Vol.41 No.2
In this paper, we introduce metallic maps between metallic Riemannian manifolds, provide an example and obtain certain conditions for such maps to be totally geodesic. We also give a sufficient condition for a map between metallic Riemannian manifolds to be harmonic map. Then we investigate the constancy of certain maps between metallic Riemannian manifolds and various manifolds by imposing the holomorphic-like condition. Moreover, we check the reverse case and show that some such maps are constant if there is a condition for this.
Remarks on metallic maps between metallic Riemannian manifolds and constancy of certain maps
Mehmet Akif Akyol 호남수학회 2019 호남수학학술지 Vol.41 No.2
In this paper, we introduce metallic maps between metallic Riemannian manifolds, provide an example and obtain certain conditions for such maps to be totally geodesic. We also give a sufficient condition for a map between metallic Riemannian manifolds to be harmonic map. Then we investigate the constancy of certain maps between metallic Riemannian manifolds and various manifolds by imposing the holomorphic-like condition. Moreover, we check the reverse case and show that some such maps are constant if there is a condition for this.
SHARP INEQUALITIES INVOLVING THE CHEN-RICCI INEQUALITY FOR SLANT RIEMANNIAN SUBMERSIONS
Mehmet Akif Akyol,Nergiz (Onen) Poyraz 대한수학회 2023 대한수학회보 Vol.60 No.5
Main objective of the present paper is to establish Chen inequalities for slant Riemannian submersions in contact geometry. In this manner, we give some examples for slant Riemannian submersions and also investigate some curvature relations between the total space, the base space and fibers. Moreover, we establish Chen-Ricci inequalities on the vertical and the horizontal distributions for slant Riemannian submersions from Sasakian space forms.
Ƞ-RICCI SOLITONS ON TRANS-SASAKIAN MANIFOLDS WITH QUARTER-SYMMETRIC NON-METRIC CONNECTION
( Oğuzhan Bahadir ),( Mohd Danish Siddiqi ),( Mehmet Akif Akyol ) 호남수학회 2020 호남수학학술지 Vol.42 No.3
In this paper, firstly we discuss some basic axioms of trans Sasakian manifolds. Later, the trans-Sasakian manifold with quarter symmetric non-metric connection are studied and its cur- vature tensor and Ricci tensor are calculated. Also, we study the Ƞ-Ricci solitons on a Trans-Sasakian Manifolds with quarter- symmetric non-metric connection. Indeed, we investigated that the Ricci and Ƞ-Ricci solitons with quarter-symmetric non-metric con- nection satisfying the conditions □.□ = 0. In a particular case, when the potential vector field ξ of the Ƞ-Ricci soliton is of gradi- ent type ξ = grad(ψ), we derive, from the Ƞ-Ricci soliton equation, a Laplacian equation satisfied by ψ. Finally, we furnish an exam- ple for trans-Sasakian manifolds with quarter-symmetric non-metric connection admitting the Ƞ-Ricci solitons.