¹Universidad Nacional de Colombia, Bogotá, Colombia. Email: tapiens@gmail.com

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

Key words: Curvature tensors, mean curvature flow.

Se obtienen las ecuaciones de evolución para el tensor de Riemann, el tensor de Ricci y el escalar de curvatura inducidas por el flujo de curvatura media. La evolución de la curvatura escalar es similar al flujo de Ricci, sin embargo, la curvatura negativa, en vez de la positiva, es favorecida. Nuestros resultados son válidos en cualquier dimensión.

Palabras clave: Tensores de curvatura, flujo de curvatura media.

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