• On the Mean Curvature of Semi-Riemannian Graphs in Semi-Riemannian Warped Products

    • Fulltext

       

        Click here to view fulltext PDF


      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/122/03/0385-0397

    • Keywords

       

      Mean curvature; semi-Riemannian graphs; semi-Riemannian warped product; Heinz–Chern type inequality.

    • Abstract

       

      We investigate the mean curvature of semi-Riemannian graphs in the semi-Riemannian warped product $M\times f\mathbb{R}_\varepsilon$, where 𝑀 is a semi-Riemannian manifold, $\mathbb{R}_\varepsilon$ is the real line $\mathbb{R}$ with metric $\varepsilon dt^2(\varepsilon =\pm 1)$, and $f:M\to \mathbb{R}^+$ is the warping function. We obtain an integral formula for mean curvature and some results dealing with estimates of mean curvature, among these results is a Heinz–Chern type inequality.

    • Author Affiliations

       

      Zonglao Zhang1

      1. College of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, People’s Republic of China
    • Dates

       
  • Proceedings – Mathematical Sciences | News

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

© 2017-2019 Indian Academy of Sciences, Bengaluru.