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

2019/08/01 by Hamed, Mohamed H. A., Massamba, Fortuné, Ssekajja, Samuel
#Differential Geometry (math.DG) #FOS: Mathematics #Null manifold #Ricci flow-type #Screen integrable distribution

paper · doi:10.48550/arxiv.1908.00263

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.

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