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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 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.