Yazar "Akyol, Mehmet Akif" seçeneğine göre listele

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  • Küçük Resim Yok
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    Conformal anti-invariant submersions from almost Hermitian manifolds
    (Tubitak Scientific & Technological Research Council Turkey, 2016) Akyol, Mehmet Akif; Sahin, Bayram
    We introduce conformal anti-invariant submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations that arose from the definition of a conformal submersion, and find necessary and sufficient conditions for a conformal anti-invariant submersion to be totally geodesic. We also check the harmonicity of such submersions and show that the total space has certain product structures. Moreover, we obtain curvature relations between the base space and the total space, and find geometric implications of these relations.
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    Conformal semi-invariant submersions
    (World Scientific Publ Co Pte Ltd, 2017) Akyol, Mehmet Akif; Sahin, Bayram
    As a generalization of semi-invariant submersions, we introduce conformal semi-invariant submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations which arise from the definition of a conformal submersion and show that there are certain product structures on the total space of a conformal semi-invariant submersion. Moreover, we also check the harmonicity of such submersions and find necessary and sufficient conditions of a conformal semi-invariant submersion to be totally geodesic.
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    Golden maps between Golden Riemannian manifolds and constancy of certain maps
    (Univ Osijek, Dept Mathematics, 2014) Sahin, Bayram; Akyol, Mehmet Akif
    We first introduce Golden maps between Golden Riemannian manifolds, give an example and show that such map is harmonic. Then we investigate the constancy of certain maps from Golden Riemannian manifolds to various manifolds by imposing the holomorphic-like map condition. Then we consider the reverse case and show that all such maps are constant.
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    Kompleks geometride konform submersiyonlar
    (İnönü Üniversitesi, 2015) Akyol, Mehmet Akif
    Doktora tezi olarak hazırlanan bu çalışma beş¸ bölümden oluşmaktadır. Birinci bölümde, konunun tarihsel gelişimi ve bu tezde ele alınan problemlerin tanıtımı yapılmaktadır. İkinci bölümde diğer bölümlere faydalı olacak temel tanım ve kavramlar ele alınmaktadır. Üçüncü bölümde, konform anti-invaryant submersiyonlar çalışılmaktadır. Hemen hemen Hermityen manifoldlardan Riemann manifoldlarına konform anti-invaryant submersiyon tanımlanmakta ve örnekler verilmektedir. Bu submersiyonlar için distribüsyonların integrallenebilirliği ve parallelliği elde edilip, submersiyonun harmonikliği ve tamamen jeodezik olma durumları incelenmektedir. Daha sonra bu tür submersiyonların belirlediği ayrışım teoremleri elde edilmektedir. Ayrıca, bir konform anti-invaryant submersiyonun total uzay, baz uzay ve liflerinin kesit eğrilikleri arasındaki ilişki araştırılmaktadır. Dördüncü bölümde, konform yarı-invaryant submersiyonlar çalışılmaktadır. Hemen hemen Hermityen manifoldlardan Riemann manifoldlarına konform yarı-invaryant submersiyon tanımlanmakta ve örnekler verilmektedir. Bu submersiyonlar için distribüsyonların integrallenebilirliği ve parallelliği incelenmektedir. Ayrıca, bu tür submersiyonların harmonikliği ve tamamen jeodezik olma durumları incelenmektedir. Beşinci bölümde, konform slant submersiyonlar çalışılmaktadır. Hemen hemen Hermityen manifoldlardan Riemann manifoldlarına konform slant submersiyon tanımlanmakta ve örnekler verilmektedir. Ayrıca bu tür submersiyonların harmonikliği ve tamamen jeodezik olma durumları ile distribüsyonların integrallenebilirliği ve paralelliği incelenmektedir.
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    A NOTE ON QUASI BI-SLANT SUBMANIFOLDS OF COSYMPLECTIC MANIFOLDS
    (Ankara Univ, Fac Sci, 2020) Akyol, Mehmet Akif; Beyendi, Selahattin
    The aim of the present paper is to define and study the notion of quasi bi-slant submanifolds of almost contact metric manifolds. We mainly concerned with quasi bi-slant submanifolds of cosymplectic manifolds as a generalization of slant, semi-slant, hemi-slant, bi-slant and quasi hemi-slant submanifolds. First, we give non-trivial examples in order to demostrate the method presented in this paper is effective and investigate the geometry of distributions. Moreover, We study these types of submanifolds with parallel canonical structures.
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    On Pointwise Quasi Bi-Slant Submanifolds
    (Univ Nis, Fac Sci Math, 2022) Akyol, Mehmet Akif; Beyendi, Selahattin; Fatima, Tanveer; Ali, Akram
    In this paper, we introduce a new class of submanifolds which are called pointwise quasi bi-slant submanifolds in almost Hermitian manifolds which extends quasi bi-slant, bi-slant, hemi-slant, semi-slant and slant submanifolds in a very natural way. Several basic results in this respect are proved in this paper. Moreover, we obtain some conditions of the distributions which is involved in the definition of the new submanifolds. We also get some results for totally geodesic and mixed totally geodesic conditions for pointwise quasi bi-slant submanifolds. Finally, we illustrate some examples in order to guarantee the new kind of submanifolds.
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    Optimal Inequalities for Hemi-Slant Riemannian Submersions
    (Mdpi, 2022) Akyol, Mehmet Akif; Demir, Ramazan; Poyraz, Nergiz Onen; Vilcu, Gabriel-Eduard
    In the present paper, we establish some basic inequalities involving the Ricci and scalar curvature of the vertical and the horizontal distributions for hemi-slant submersions having the total space a complex space form. We also discuss the equality case of the obtained inequalities and provide illustrative examples.
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    Pointwise quasi hemi-slant submanifolds
    (Univ Nis, Fac Sci Math, 2023) Beyendi, Selahattin; Akyol, Mehmet Akif; Stankovic, Mica S.
    The objective of this paper is to introduce a new class of submanifolds which are called pointwise quasi hemi-slant submanifolds in almost Hermitian manifolds which extends quasi hemi-slant, hemi-slant, semi-slant and slant submanifolds in a very natural way. Several basic results in this respect are proved in this paper. Moreover, we obtain some conditions of the distributions which are involved in the definition of the new submanifolds. We also get some results for totally geodesic and mixed totally geodesic conditions for pointwise quasi hemi-slant submanifolds. Finally, we illustrate some examples in order to guaranty the new kind of submanifolds.
  • Küçük Resim Yok
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    Ricci and scalar curvature inequalities for semi-slant Riemannian submersions in complex space forms
    (World Scientific Publ Co Pte Ltd, 2023) Poyraz, Nergiz (Onen); Akyol, Mehmet Akif; Demir, Ramazan
    This paper is devoted to the obtain Chen inequalities containing the Ricci and scalar inequalities on the vertical and the horizontal distributions for semi-slant Riemannian submersions from complex space forms onto Riemannian manifolds. The equality case of the obtained inequalities is discussed. At the end, some geometric consequences are obtained. Moreover, many examples are constructed.