A Ricci-type flow on globally null manifolds and its gradient estimates

Authors

  • Mohamed H. A. Hamed School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsville 3209, South Africa
  • Fortuné Massamba University of KwaZulu-Natal http://orcid.org/0000-0002-6922-3566
  • Samuel Ssekajja School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsville 3209, South Africa

DOI:

https://doi.org/10.33044/revuma.1874

Abstract

Locally, a screen integrable globally null manifold $M$ splits through a Riemannian leaf $M'$ of its screen distribution and a null curve $\mathcal{C}$ tangent to its radical distribution. The leaf $M'$ carries a lot of geometric information about $M$ and, in fact, forms a basis for the study of expanding and non-expanding horizons in black hole theory. In the present paper, we introduce a degenerate Ricci-type flow in $M'$ via the intrinsic Ricci tensor of $M$. Several new gradient estimates regarding the flow are proved.

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Author Biography

Fortuné Massamba, University of KwaZulu-Natal

School of Mathematics, Statistics and Computer Science and Associate Professor

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Published

2021-09-29

Issue

Vol. 62 No. 2 (2021)

Section

Article

License

Copyright (c) 2022 Mohamed H. A. Hamed, Fortuné Massamba, Samuel Ssekajja

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