10.1007/s40096-021-00423-3

Some concave functions on Lorentzian manifolds

  • Reza Mirzaie*1,
  • Omid Rezaei1,
  1. Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University (IKIU), Qazvin, IR

Published in Issue 2021-07-23

How to Cite

Mirzaie, R., & Rezaei, O. (2021). Some concave functions on Lorentzian manifolds. Mathematical Sciences, 16(3 (September 2022). https://doi.org/10.1007/s40096-021-00423-3
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Abstract

Abstract Let M be a Lorentzian manifold and ϕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi$$\end{document} be a future timelike isometry of M . We use ϕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi$$\end{document} to construct a concave function fϕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_{\phi }$$\end{document} on M under some conditions on the curvature of timelike and spacelike planes. As a topological application, we characterize the fundamental group of M , when M has positive curvature along timelike planes.

Keywords

  • Lorentzian manifold,
  • Concave function,
  • Timelike plane,
  • Future timelike isometry

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