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Revista de la
Unión Matemática Argentina
A Ricci-type flow on globally null manifolds and its gradient estimates
Mohamed H. A. Hamed, Fortuné Massamba, and Samuel Ssekajja
Volume 62, no. 2 (2021), pp. 327–349    

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

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Abstract

Locally, a screen integrable globally null manifold M splits through a Riemannian leaf M′ of its screen distribution and a null curve 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.