Sharp Growth Estimates for Warping Functions in Multiply Warped Product Manifolds

IF 0.5 Q4 PHYSICS, MATHEMATICAL

Journal of Geometry and Symmetry in Physics Pub Date : 2018-09-15 DOI:10.7546/JGSP-52-2019-27-46

Bang‐Yen Chen, S. Wei

引用次数: 15

Abstract

By applying an average method in PDE, we obtain a dichotomy between "constancy" and "infinity" of the warping functions on complete noncompact Riemannian manifolds for an appropriate isometric immersion of a multiply warped product manifold $N_1\times_{f_2} N_2 \times \cdots \times _{f_k} N_k\, $ into a Riemannian manifold. Generalizing the earlier work of the authors in [{Glasg. Math. J. 51 (2009) 579-592], we establish sharp inequalities between the mean curvature of the immersion and the sectional curvatures of the ambient manifold under the influence of quantities of a purely analytic nature (the growth of the warping functions). Several applications of our growth estimates are also presented.

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多重Warped乘积流形中Warping函数的Sharp Growth估计

通过在PDE中应用平均方法，我们得到了完全非紧黎曼流形上的翘曲函数的“恒定性”和“无穷大”之间的二分法，用于乘积翘曲乘积流形$N_1\times_{f_2}N_2\times\cdots\times_{f _k}N_k\，$到黎曼流形的适当等距浸入。推广作者在〔｛Glasg.Math.J.51（2009）579-592〕中的早期工作，我们在纯分析性质的量（翘曲函数的增长）的影响下，在浸入的平均曲率和环境流形的截面曲率之间建立了尖锐的不等式。还介绍了我们的增长估计的几个应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Geometry and Symmetry in Physics PHYSICS, MATHEMATICAL-

CiteScore

1.50

自引率

25.00%

发文量

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