Mean Curvature Driven Ricci Flow

Abstract

We obtain the evolution equations for the Riemann tensor, the Ricci tensor and the scalar curvature induced by the mean curvature flow. The evolution for the scalar curvature is similar to the Ricci flow, however, negative, rather than positive, curvature is preserved. Our results are valid in any dimension.

References in corpus (1)

• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds