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    A class of Ricci-flat Finsler metrics
    (Polish Acad Sciences Inst Mathematics-Impan, 2018) Ulgen, Semail; Sevim, Esra S.
    We study a class of Ricci-flat Finsler metrics formed by a Riemannian metric and a 1-form. We discuss some special singular solutions.
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    On a Class of Ricci Quadratic Finsler Metrics
    (Springer Heidelberg, 2024) Gabrani, Mehran; Sevim, Esra Sengelen; Ulgen, Semail
    In this paper, we study a class of Finsler warped product metrics with quadratic Ricci curvature. This class is characterized by a partial differential equation. In particular, we obtain a special class of Finsler warped product metrics with quadratic Ricci curvature, indeed, the metrics in this class are Einstein but not Ricci flat. We find an equation that characterizes Finsler warped product metrics as a strongly Ricci-quadratic.
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    On Einstein Finsler metrics
    (World Scientific Publ Co Pte Ltd, 2021) Ulgen, Semail; Sevim, Esra Sengelen; Hacinliyan, Irma
    In this paper, we study Finsler metrics expressed in terms of a Riemannian metric, a 1-form, and its norm and find equations with sufficient conditions for such Finsler metrics to become Ricci-flat. Using certain transformations, we show that these equations have solutions and lead to the construction of a large and special class of Einstein metrics.
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    On Some Ricci Curvature Tensors in Finsler Geometry
    (Springer Basel Ag, 2023) Sevim, Esra Sengelen; Shen, Zhongmin; Ulgen, Semail
    In this paper, we discuss several Ricci curvature tensors and their relationship with the Ricci curvature and some non-Riemannian quantities. By these Ricci curvature tensors, we shall have a better understanding on the non-Riemannian quantities.
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    On strongly Ricci-Quadratic Finsler Metrics
    (Springer, 2023) Sevim, Esra Sengelen; Shen, Zhongmin; Ulgen, Semail
    Finsler metrics being Ricci-quadratic is a non-Riemannian condition since the Ricci curvature (tensor) is always Ricci-quadratic for Riemannian metrics. In this paper, we introduce the notion of strongly Ricci-quadratic Finsler metrics. We classify strongly Ricci-quadratic Randers metrics expressed in a navigation form.
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    Some Ricci-flat (?, ?)-metrics
    (Springer, 2016) Sevim, Esra Sengelen; Ulgen, Semail
    In this paper, we study a special class of Finsler metrics, (alpha, beta)-metrics, defined by F = alpha phi(beta/alpha), where alpha is a Riemannian metric and beta is a 1-form. We find an equation that characterizes Ricci -flat (a, fl) -metrics under the condition that the length of beta with respect to a is constant.