芬斯勒流形上的两个重要不等式  

Two Important Inequalities on Finsler Manifolds

作　　者：程新跃 张希滨 CHENG Xinyue;ZHANG Xibin(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《西南师范大学学报（自然科学版）》2023年第1期32-39,共8页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11871126);重庆师范大学研究基金项目(17XLB022)。

摘　　要：主要研究了芬斯勒几何中的Poincare-Lichnerowicz不等式和Laplacian第一特征值的下界估计.通过使用积分型Bochner公式及其相关的不等式,在加权Ricci曲率RicN有正下界的条件下得到了两个重要的不等式,改进了芬斯勒流形上的两个已知的重要结果.In this paper, we concentrate on studying Poincare-Lichnerowicz inequality and the lower bound estimation of the Laplacian first eigenvalue in Fensler geometry. By applying the integral Bochner formula and its related inequalities, we obtain two important inequalities under the condition that the weighted Ricci curvature RicNhas a positive lower bound. As a result, our results improve two known important inequalities on the Finsler manifold.

关 键 词：芬斯勒流形 加权Ricci曲率 Bochner公式 Poincare-Lichnerowicz不等式 第一特征值 

分 类 号：O186.1[理学—数学]