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Null hypersurfaces evolved by their mean curvature in a Lorentzian manifold

Volume 157 / 2019

Fortuné Massamba, Samuel Ssekajja Colloquium Mathematicum 157 (2019), 83-106 MSC: Primary 53C50; Secondary 53C44, 53C40. DOI: 10.4064/cm7450-8-2018 Published online: 1 March 2019

Abstract

We use null isometric immersions to introduce time-dependent null hypersurfaces, in a Lorentzian manifold, evolving in the direction of their mean curvature vector (a vector transversal to the null hypersurface). We prove an existence result for such hypersurfaces in a short-time interval. Then, we discuss the evolution of some induced geometric objects. Consequently, we prove under certain geometric conditions that some of the above objects will blow-up in finite time. Also, several examples are given to illustrate the main ideas.

Authors

  • Fortuné MassambaSchool of Mathematics, Statistics and Computer Science
    University of KwaZulu-Natal
    Private Bag X01
    Scottsville 3209, South Africa
    e-mail
  • Samuel SsekajjaSchool of Mathematics, Statistics and Computer Science
    University of KwaZulu-Natal
    Private Bag X01
    Scottsville 3209, South Africa
    e-mail

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