Browsing by Author "Cheng, Xinyue"

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    Einstein Finsler Metrics and Killing Vector Fields on Riemannian Manifolds
    (Springer, 2017-01) Cheng, Xinyue; Shen, Zhongmin; Department of Mathematical Sciences, School of Science
    We use a Killing form on a Riemannian manifold to construct a class of Finsler metrics. We find equations that characterize Einstein metrics among this class. In particular, we construct a family of Einstein metrics on S3 with Ric = 2F2, Ric = 0 and Ric = -2F2, respectively. This family of metrics provides an important class of Finsler metrics in dimension three, whose Ricci curvature is a constant, but the flag curvature is not.
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    Some Inequalities on Finsler Manifolds with Weighted Ricci Curvature Bounded Below
    (Springer, 2022-02-07) Cheng, Xinyue; Shen, Zhongmin; Mathematical Sciences, School of Science
    We establish some important inequalities under a lower weighted Ricci curvature bound on Finsler manifolds. Firstly, we establish a relative volume comparison of Bishop–Gromov type. As one of the applications, we obtain an upper bound for volumes of the Finsler manifolds. Further, when the S-curvature is bounded on the whole manifold, we obtain a theorem of Bonnet–Myers type on Finsler manifolds. Finally, we obtain a sharp Poincaré–Lichnerowicz inequality by using integrated Bochner inequality, from which we obtain a better lower bound for the first eigenvalue on the Finsler manifolds.