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arXiv · 1706.09368

Ricci-Yamabe maps for Riemannian flows and their volume variation and volume entropy

Mircea Crasmareanu·Sinem Güler
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Abstract

The aim of this short note is to produce new examples of geometrical flows associated to a given Riemannian flow $g(t)$. The considered flow in covariant symmetric $2$-tensor fields will be called Ricci-Yamabe map since it involves a scalar combination of Ricci tensor and scalar curvature of $g(t)$. Due to the signs of considered scalars the Ricci-Yamabe flow can be also a Riemannian or semi-Riemannian or singular Riemannian flow. We study the associated function of volume variation as well as the volume entropy. Finally, since the two-dimensional case was the most handled situation we express the Ricci flow equation in all four orthogonal separable coordinate systems of the plane.

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Mircea Crasmareanu, Sinem Güler. 2017-06-28. Ricci-Yamabe maps for Riemannian flows and their volume variation and volume entropy. https://arxiv.org/abs/1706.09368

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