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Öğe Conformal slant submersions from cosymplectic manifolds(TUBITAK, 2018) Gündüzalp, Yılmaz; Akyol, Mehmet AkifAkyol [Conformal anti-invariant submersions from cosymplectic manifolds, Hacettepe Journal of Mathematics and Statistics 2017; 462: 177-192] defined and studied conformal antiinvariant submersions from cosymplectic manifolds. The aim of the present paper is to define and study the notion of conformal slant submersions (it means the Reeb vector field ξ is a vertical vector field) from cosymplectic manifolds onto Riemannian manifolds as a generalization of Riemannian submersions, horizontally conformal submersions, slant submersions, and conformal antiinvariant submersions. More precisely, we mention many examples and obtain the geometries of the leaves of vertical distribution and horizontal distribution, including the integrability of the distributions, the geometry of foliations, some conditions related to total geodesicness, and harmonicity of the submersions. Finally, we consider a decomposition theorem on the total space of the new submersion.Öğe Pointwise hemi-slant Riemannian maps ($\mathcal{PHSRM}$) from almost Hermitian manifolds(Hacettepe Üniversitesi, 2024) Akyol, Mehmet Akif; Gündüzalp, YılmazIn 2022, the notion of pointwise slant Riemannian maps were introduced by Y. Gündüzalp and M. A. Akyol in [J. Geom. Phys. {179}, 104589, 2022] as a natural generalization of slant Riemannian maps, slant Riemannian submersions, slant submanifolds. As a generalization of pointwise slant Riemannian maps and many subclasses notions, we introduce pointwise hemi-slant Riemannian maps (briefly, $\mathcal{PHSRM}$) from almost Hermitian manifolds to Riemannian manifolds, giving a figure which shows the subclasses of the map and a non-trivial (proper) example and investigate some properties of the map, we deal with their properties: the J-pluriharmonicity, the J-invariant, and the totally geodesicness of the map. Finally, we study some curvature relations in complex space form, involving Chen inequalities and Casorati curvatures for $\mathcal{PHSRM}$, respectively.Öğe Pointwise hemi-slant Riemannian maps (PHSRM) from almost Hermitian manifolds(Hacettepe Univ, Fac Sci, 2024) Akyol, Mehmet Akif; Gunduzalp, YilmazIn 2022, the notion of pointwise slant Riemannian maps were introduced by Y. G & uuml;nd & uuml;zalp and M. A. Akyol in [J. Geom. Phys. 179, 104589, 2022] as a natural generalization of slant Riemannian maps, slant Riemannian submersions, slant submanifolds. As a generalization of pointwise slant Riemannian maps and many subclasses notions, we introduce p ointwise hemi-slant Riemannian maps (briefly, PHSRM) ) from almost Hermitian manifolds to Riemannian manifolds, giving a figure which shows the subclasses of the map and a non-trivial (proper) example and investigate some properties of the map, we deal with their properties: the J-pluriharmonicity, the J-invariant, and the totally geodesicness of the map. Finally, we study some curvature relations in complex space form, involving Chen inequalities and Casorati curvatures for PHSRM, respectively.Öğe Pointwise semi-slant Riemannian (PSSR) maps from almost Hermitian manifolds(Univ Nis, Fac Sci Math, 2023) Gunduzalp, Yilmaz; Akyol, Mehmet AkifIn this paper, as a generalization of pointwise slant submanifolds [B-Y. Chen and O. J. Garay, Pointwise slant submanifolds in almost Hermitian manifolds, Turk J Math 36, (2012), 630-640.], pointwise slant submersions [J.W.Lee and B. S.ahin, Pointwise slant submersions, Bulletin of the Korean Mathematical Sosiety, 51(4), (2014), 115-1126.] and pointwise slant Riemannian maps [Y. Gu center dot ndu center dot zalp and M. A. Akyol, Pointwise slant Riemannian maps from Kaehler manifolds, Journal of Geometry and Physics, 179, (2002), 104589.], we introduce pointwise semi-slant Riemannian maps (briefly, PSSR maps) from almost Hermitian manifolds to Riemannian manifolds, present examples and characterizations. We also investigate the harmonicity of such maps. Moreover, we give Chen-Ricci inequality for a PSSR map. Finally, we study some curvature relations in complex space forms, involving Casorati curvatures for PSSR maps.Öğe Pointwise Slant Riemannian Maps (PSRM) to almost hermitian manifolds(Birkhauser, 2023) Akyol, Mehmet Akif; Gündüzalp, YılmazThe aim of the present paper is to introduce new class of Riemannian maps which are called pointwise slant Riemannian maps (briefly, PSRM) as a natural generalization of pointwise slant submanifolds which were introduced by Chen and Garay (Turkish J Math 36:630–640, 2012) and pointwise slant submersions which were defined by Lee and S¸ahin (Bull Korean Math Soc 51(4):1115–1126, 2014]. We mention many examples and investigate the geometry of foliations which are arisen from the definition of a PSRM and obtain decomposition theorems using the existence of PSRM. Moreover, we find necessary and sufficient conditions for PSRM to be totally geodesic and investigate the harmonicity of such maps. Finally, we get two inequalities in terms of the second fundamental form of a PSRM and check the equality case.Öğe Pointwise slant Riemannian maps from Kaehler manifolds(Elsevier B.V., 2022) Gündüzalp, Yılmaz; Akyol, Mehmet AkifPointwise slant submanifolds were introduced by Chen and Garay (2012) [16] as a natural generalization of slant submanifolds. On the other hand, pointwise slant submersions were defined by Lee and Şahin (2014) [29] as a natural generalization of slant submersions. In this paper, as a generalization of pointwise slant submanifolds and pointwise slant submersions, we introduce pointwise slant Riemannian maps from almost Hermitian manifolds to Riemannian manifolds, present examples and characterizations. We investigate the geometry of foliations which are arisen from the definition of a pointwise slant Riemannian map and obtain decomposition theorems by using the existence of pointwise slant Riemannian maps. We also investigate the harmonicity of such maps and find necessary and sufficient conditions for pointwise slant Riemannian maps to be totally geodesic. Finally, we study some curvature relations in complex space forms, involving Casorati curvatures for pointwise slant Riemannian maps.Öğe Remarks on conformal anti-invariant Riemannian maps to cosymplectic manifolds(Hacettepe University Faculty of Science, 2021) Gündüzalp, Yılmaz; Akyol, Mehmet AkifM.A. Akyol and B. Şahin [Conformal anti-invariant Riemannian maps to Kaehler manifolds, U.P.B. Sci. Bull., Series A, Vol. 80, Iss. 4, 2018] defined and studied the notion of conformal anti-invariant Riemannian maps to Kaehler manifolds. In this paper, as a generalization of totally real submanifolds and anti-invariant Riemannian maps, we extend this notion to almost contact metric manifolds. In this manner, we introduce conformal anti-invariant Riemannian maps from Riemannian manifolds to cosymplectic manifolds. In order to guarantee the existence of this notion, we give a non-trivial example, investigate the geometry of foliations which are arisen from the definition of a conformal Riemannian map and obtain decomposition theorems by using the existence of conformal Riemannian maps. Moreover, we investigate the harmonicity of such maps and find necessary and sufficient conditions for conformal anti-invariant Riemannian maps to be totally geodesic. Finally, we study weakly umbilical conformal Riemannian maps and obtain a classification theorem for conformal anti-invariant Riemannian maps.Öğe SEMI-INVARIANT SEMI-RIEMANNIAN SUBMERSIONS(Ankara Univ, Fac Sci, 2018) Akyol, Mehmet Akif; Gunduzalp, YilmazIn this paper, we introduce semi-invariant semi-Riemannian sub-mersions from para-Kahler manifolds onto semi-Riemannian manifolds. We give some examples, investigate the geometry of foliations that arise from the definition of a semi-Riemannian submersion and check the harmonicity of such submersions. We also find necessary and sufficient conditions for a semi invariant semi-Riemannian submersion to be totally geodesic. Moreover, we obtain curvature relations between the base manifold and the total manifold.Öğe Some inequalities for bi-slant Riemannian submersions in complex space forms(World Scientific Publ Co Pte Ltd, 2024) Poyraz, Nergiz (Onen); Gunduzalp, Yilmaz; Akyol, Mehmet AkifThe goal of this paper is to analyze sharp-type inequalities including the scalar and Ricci curvatures of bi-slant Riemannian submersions in complex space forms. Then, for bi-slant Riemannian submersion between a complex space form and a Riemannian manifold, we give inequalities involving the Casorati curvature of the space ker phi*. Also, we mention some examples.
