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

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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.