Browsing by Subject "weighted Ricci curvature"

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    On a class of weakly weighted Einstein metrics
    (World Scientific, 2022-09) Shen, Zhongmin; Zhao, Runzhong; Mathematical Sciences, School of Science
    The notion of general weighted Ricci curvatures appears naturally in many problems. The N-Ricci curvature and the projective Ricci curvature are just two special ones with totally different geometric meanings. In this paper, we study general weighted Ricci curvatures. We find that Randers metrics of certain isotropic weighted Ricci curvature must have isotropic S-curvature. Then we classify them via their navigation expressions. We also find equations that characterize Randers metrics of almost isotropic weighted Ricci curvature.
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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.