Yazar "Polat, Murat" seçeneğine göre listele

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    B. Y. Chen-Ricci inequalities for anti-invariant Riemannian submersions in Kenmotsu space forms
    (Springer Heidelberg, 2024) Polat, Murat
    The aim of the present paper is to analyze sharp type inequalities including the scalar and Ricci curvatures of anti-invariant Riemannian submersions in Kenmotsu space forms K-s(epsilon). We give non-trivial examples for anti-invariant Riemannian submersions, investigate some curvature relations between the total space and fibres according to vertical and horizontal cases of xi. Moreover, we acquire Chen-Ricci inequalities on the ker theta(*) and (ker theta(*))(perpendicular to) distributions for anti-invariant Riemannian submersions from Kenmotsu space forms according to vertical and horizontal cases of xi.
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    Chen-Ricci inequalities in slant submersions for complex space forms
    (University of Nis, 2022) Gündüzalp, Yılmaz; Polat, Murat
    The goal of the present paper is to analyze sharp type inequalities including the scalar and Ricci curvatures of slant submersions in complex space forms.
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    Clairaut Pointwise Slant Submersion from Locally Product Riemannian Manifolds
    (Kazım İLARSLAN, 2023) Polat, Murat
    The goal of the present paper is to analyze some geometric features of Clairaut pointwise slant submersions whose total manifold is a locally product Riemannian manifold. We describe Clairaut pointwise slant submersions from locally product Riemannian manifold onto a Riemannian manifold. We study pointwise slant submersions by providing a consequent which defines the geodesics on the total space of this type submersions. We also give a non-trivial example of the Clairaut pointwise slant submersions whose total manifolds are locally product Riemannian.
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    Clairaut pointwise slant submersions from locally product riemannian manifolds
    (DergiPark, 2023) Polat, Murat
    In this paper, we consider pointwise slant submersions from locally product Riemannian manifolds. We first give a necessary and sufficient condition for a curve on the total manifold to be a geodesic and then focus investigate new Clairaut conditions for considered submersion. In a main theorem, we find a new necessary and sufficient condition for a pointwise slant submersion to be Clairaut in case of its total manifold is locally product Riemannian manifold. Finally, we present an illustrative example for this kind of submersion which satisfies Clairaut condition.
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    Clairaut semi invariant submersions from locally product Riemannian manifolds
    (Erzincan Binali Yıldırım Üniversitesi, Fen Bilimleri Enstitüsü, 2023) Polat, Murat
    The purpose of this article is to analyze geometric features of Clairaut semi-invariant Riemannian submersions whose total manifolds are locally product Riemannian manifold and investigate fundamental results on such submersion. We also ensure an explicit example of Clairaut semi-invariant Riemannian submersion.
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    Clairaut semi-invariant riemannian maps to kähler manifolds
    (Birkhauser, 2024) Polat, Murat; Meena, Kiran
    In this paper, first, we recall the notion of Clairaut Riemannian map (CRM) F using a geodesic curve on the base manifold and give the Ricci equation. We also show that if base manifold of CRM is space form then leaves of (kerF∗)⊥ become space forms and symmetric as well. Secondly, we define Clairaut semi-invariant Riemannian map (CSIRM) from a Riemannian manifold (M,gM) to a Kähler manifold (N,gN,P) with a non-trivial example. We find necessary and sufficient conditions for a curve on the base manifold of semi-invariant Riemannian map (SIRM) to be geodesic. Further, we obtain necessary and sufficient conditions for a SIRM to be CSIRM. Moreover, we find necessary and sufficient condition for CSIRM to be harmonic and totally geodesic. In addition, we find necessary and sufficient condition for the distributions D1¯ and D2¯ of (kerF∗)⊥ (which are arisen from the definition of CSIRM) to define totally geodesic foliations. Finally, we obtain necessary and sufficient conditions for (kerF∗)⊥ and base manifold to be locally product manifold D1¯×D2¯ and (rangeF∗)×(rangeF∗)⊥, respectively.
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    Clairaut slant Riemannian maps to Kahler manifolds
    (World Scientific Publ Co Pte Ltd, 2023) Yadav, Jyoti; Shanker, Gauree; Polat, Murat
    The aim of this paper is to study the idea of Clairaut slant Riemannian maps from Riemannian manifolds to Kahler manifolds. First, for the slant Riemannian map, we obtain the necessary and sufficient conditions for a curve to be a geodesic on the base manifold. Further, we find the necessary and sufficient conditions for the slant Riemannian map to be a Clairaut slant Riemannian map; for Clairaut slant Riemannian map to be totally geodesic; for the base manifold to be a locally product manifold. Further, we obtain the necessary and sufficient condition for the integrability of range of derivative map. Also, we investigate the harmonicity of Clairaut slant Riemannian map. Finally, we get two inequalities in terms of second fundamental form of a Clairaut slant Riemannian map and check the equality case.
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    A combination of Lie group-based high order geometric integrator and delta-shaped basis functions for solving Korteweg-de Vries (KdV) equation
    (World Scientific Publication, 2021) Polat, Murat; Oruç, Ömer
    In this work, we develop a novel method to obtain numerical solution of well-known Korteweg-de Vries (KdV) equation. In the novel method, we generate differentiation matrices for spatial derivatives of the KdV equation by using delta-shaped basis functions (DBFs). For temporal integration we use a high order geometric numerical integrator based on Lie group methods. This paper is a first attempt to combine DBFs and high order geometric numerical integrator for solving such a nonlinear partial differential equation (PDE) which preserves conservation laws. To demonstrate the performance of the proposed method we consider five test problems. We reckon L-infinity, L-2 and root mean square (RMS) errors and compare them with other results available in the literature. Besides the errors, we also monitor conservation laws of the KDV equation and we show that the method in this paper produces accurate results and preserves the conservation laws quite good. Numerical outcomes show that the present novel method is efficient and reliable for PDEs.
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    Complete lifts of projectable linear connection to semi-tangent bundle
    (The Honam Mathematical Society, 2021) Polat, Murat; Yıldırım, Furkan
    We study the complete lifts of projectable linear connection for semi-tangent bundle. The aim of this study is to establish relations between these and complete lift already known. In addition, the relations between in nitesimal linear transformations and projectable linear connections are studied. We also have a new example for good square in this work.
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    A composite method based on delta-shaped basis functions and Lie group high-order geometric integrator for solving Kawahara-type equations
    (Wiley, 2023) Oruç, Ömer; Polat, Murat; 0000-0002-6655-3543; 0000-0003-1846-0817
    In this paper, we devise a novel method to solve Kawahara-type equations numerically. In this novel method, for spatial discretization, we use delta-shaped basis functions and generate differentiation matrices for spatial derivatives of the Kawahara-type equations. For discretization of temporal variable, we utilize a high-order geometric numerical integrator based on Lie group methods. For illustration of efficiency of the suggested method, we consider some test problems. We calculate errors and make some comparisons with other results that exist in literature. We also report changes in conservation laws during numerical simulations, and we indicate that the suggested method can preserve the conservation laws pretty good. Outcomes of numerical simulations indicate that the suggested method in this paper is reliable and effective for nonlinear partial differential equations (PDEs).
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    Lagrangian and Clairaut anti-invariant semi-Riemannian submersions in para-Kaehler geometry
    (Soc Paranaense Matematica, 2024) Gunduzalp, Yilmaz; Polat, Murat
    Purpose of this article is to examine some geometric features of Clairaut anti-invariant semiRiemannian submersions from para-Kaehler manifold to a Riemannian manifold. We give Lagrangian semiRiemannian submersion in para-Kaehler space froms. Then, we investigate under what conditions Clairaut submersions can become anti-invariant semi-Riemannian submersions. After, we obtain conditions for totally geodesic on vertical and horizontal distributions. We also supply a non-trivial example of Clairaut submersion.
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    SOME INEQUALITIES OF ANTI-INVARIANT RIEMANNIAN SUBMERSIONS IN COMPLEX SPACE FORMS
    (Univ Miskolc Inst Math, 2022) Gunduzalp, Yilmaz; Polat, Murat
    B.-Y. Chen revealed the intrinsic and extrinsic invariants who established an inequality including Ricci curvature and squared mean curvature of a submanifold in a real space form Rn(c) in 1999 (see [4]). In 2005 by B.-Y. Chen, a generalization of this inequality was proved for arbitrary submanifolds in an arbitrary Riemannian manifold (see [5]). Subsequently, this inequality has been comprehensively examined for different ambient spaces by some authors who are achieved some results (see [3,7, 16, 19, 22, 25]). A C infinity-submersion phi can be defined according to the following conditions: a (pseudo)-Riemannian submersion [1, 8,12,17, 20, 21], an almost Hermitian submersion [23], a quaternionic submersion [13] , a slant submersion [11], a Clairaut Submerpecially, by utilizing the notion of almost Hermitian submersions, B. Watson [23]
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    A STUDY ON CONFORMAL SEMI-INVARIANT RIEMANNIAN MAPS TO COSYMPLECTIC MANIFOLDS
    (Univ Politehnica Bucharest, Sci Bull, 2024) Polat, Murat
    In [3], Akyol and S,ahin introduced the concept of conformal semi -invariant Riemannian maps to almost Hermitian manifolds. In this article, we expand this concept to almost contact metric manifolds as a generalization of totally real submanifolds and semi -invariant Riemannian maps. Herewith, we present conformal semi -invariant Riemannian maps from Riemannian manifolds to cosymplectic manifolds. To ensure the existence of this concept, we prepare a illustrative example, investigate the geometry of the leaves of D-1, D-2,D-1 and D-2 conditions for conformal semi -invariant Riemannian maps to be totally geodesic. We also investigate the harmonicity of such maps. . We find necessary and sufficient