Yazar "Gabrani, Mehran" seçeneğine göre listele

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    A Class of Finsler Metrics with Almost Vanishing H- and ?-curvatures
    (Springer Basel Ag, 2021) Gabrani, Mehran; Rezaei, Bahman; Sevim, Esra Sengelen
    In this paper, we study Xi -curvature and H-curvature of a special class of Finsler metrics called general (alpha,beta)-metrics. We prove that every general (alpha,beta)-metric of almost vanishing H-curvature is of almost vanishing Xi -curvature under certain conditions. Moreover, we study such Finsler metric with vanishing Xi -curvature and its interaction to the flag curvature.
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    General spherically symmetric Finsler metrics with constant Ricci and flag curvature
    (Elsevier, 2021) Gabrani, Mehran; Rezaei, Bahman; Sevim, Esra Sengelen
    In this paper, we investigate the flag curvature of a special class of Finsler metrics called general spherically symmetric Finsler metrics, which are defined by a Euclidean metric and two related 1-forms. We find equations to characterize the class of metrics with constant Ricci curvature (tensor) and constant flag curvature. Moreover, we study general spherically symmetric Finsler metrics with the vanishing non-Riemannian quantity chi-curvature. In particular, we construct some new projectively flat Finsler metrics of constant flag curvature. (C) 2021 Elsevier B.V. All rights reserved.
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    ISOTROPIC MEAN BERWALD FINSLER WARPED PRODUCT METRICS
    (Korean Mathematical Soc, 2023) Gabrani, Mehran; Rezaei, Bahman; Sevim, Esra sengelen
    It is our goal in this study to present the structure of isotropic mean Berwald Finsler warped product metrics. We bring out the rich class of warped product Finsler metrics behaviour under this condition. We show that every Finsler warped product metric of dimension n >= 2 is of isotropic mean Berwald curvature if and only if it is a weakly Berwald metric. Also, we prove that every locally dually flat Finsler warped product metric is weakly Berwaldian. Finally, we prove that every Finsler warped product metric is of isotropic Berwald curvature if and only if it is a Berwald metric.
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    ON A CLASS OF FINSLER METRICS OF QUADRATIC WEYL CURVATURE
    (Tohoku University, 2023) Gabrani, Mehran; Sevim, Esra Sengelen; Shen, Zhongmin
    The class of warped product manifolds plays an important role in differential geometry and physics. In this paper, we shall study product manifolds R x ?????? with Finsler metrics arising from warped product structure. We give an equivalent condition for those metrics to be of quadratic Weyl curvature.
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    On Finsler Warped Product Metrics with Special Curvatures Properties
    (Springernature, 2022) Gabrani, Mehran; Rezaei, Bahman; Sevim, Esra Sengelen
    In this paper, we study a class of Finsler metrics called Finsler warped product metrics. We prove that every Finsler warped product metric is of isotropic E-curvature if and only if it is of isotropic S-curvature. Moreover, we prove that if the metric is of Douglas type and has isotropic S-curvature, then it must be Randers metric or Berwald metric.
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    On Landsberg Warped Product Metrics
    (B Verkin Inst Low Temperature Physics & Engineering Nas Ukraine, 2021) Gabrani, Mehran; Rezaei, Bahman; Sevim, Esra Sengelen
    In this paper, we discuss a class of Finsler metrics which are called Finsler warped product metrics. These metrics have been studied by Chen-Shen-Zhao, 2018. Basically, we study the Berwald curvature of Finsler warped product metrics. Also, we characterize the Finsler warped product metrics of isotropic Berwald curvature, then we obtain that they are Randers metrics (Theorem 1.2). Moreover, we consider an important problem which is unicorn problem in Finsler geometry for the class of Finsler metrics. In fact, we get the answer of the crucial question of this study that whether or not such a Landsberg Finsler warped product metric is a Berwald metric (Theorem 1.3).
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    On projective invariants of general spherically symmetric Finsler spaces in Rn
    (Elsevier, 2022) Gabrani, Mehran; Rezaei, Bahman; Sevim, Esra Sengelen
    In this paper we discuss projective invariants of general spherically symmetric Finsler metrics in R-n. We obtain the necessary and sufficient conditions for the metrics to be projectively Ricci flat, Weyl and W-quadratic types. In particular, we use the spray theory to give a short proof of the well-known theorem, that is, Finsler manifold is of scalar flag curvature if and only if F is Weyl metric . Therefore, considering the technique of the proof, we obtain a necessary and sufficient condition for the metrics of scalar flag curvature to be Weyl metric. Also, under a certain condition, we prove that projectively Ricci flat general spherically symmetric metrics coincide with the Douglas type metric.(c) 2022 Elsevier B.V. All rights reserved.
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    Some projectively Ricci-flat (?, ?)-metrics
    (Springer, 2023) Gabrani, Mehran; Sevim, Esra Sengelen; Shen, Zhongmin
    In this paper, we construct some projectively Ricci-flat Finsler metrics defined by a Riemannian metric a and a 1-form beta. Moreover, we classify the projectively Ricci-flat (alpha, beta)-metrics under the condition, that beta is a non-parallel Killing form which has non-zero constant length.
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    The General Spherically Symmetric Finsler Metrics with Isotropic E-Curvature
    (Natl Acad Sciences India, 2022) Gabrani, Mehran; Rezaei, Bahman; Sevim, Esra Sengelen
    In this paper, we classify general spherically symmetric Finsler metrics F=r phi(u,s,v,t) with isotropic E-curvature and isotropic S-curvature. We prove that F is of isotropic E-curvature if and only if it is of isotropic S-curvature. Moreover, as an application, we construct an explicit solution of phi of a special class of general spherically symmetric Finsler metrics F with isotropic E-curvature.
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    The S-curvature of Finsler warped product metrics
    (Elsevier, 2024) Gabrani, Mehran; Rezaei, Bahman; Sevim, Esra Sengelen
    The class of warped product metrics can often be interpreted as key space models for general theory of relativity and in the theory of space-time structure. In this paper, we study one of the most important non -Riemannian quantities in Finsler geometry which is called the S -curvature. We examined the behavior of the S -curvature in the Finsler warped product metrics. We are going to prove that every Finsler warped product metric R x Rn has almost isotropic S -curvature if and only if it is a weakly Berwald metric. Moreover, we show that every Finsler warped product metric has isotropic S -curvature if and only if S -curvature vanishes. (c) 2023 Elsevier B.V. All rights reserved.