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

Authors : Sinem Güler, Mircea Crasmareanu

Pages : 2631-2641

View : 11 | Download : 6

Publication Date : 9999-12-31

Article Type : Makaleler

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 commonly addressed situation we express the Ricci flow equation in all four orthogonal separable coordinate systems of the plane.
Keywords : Riemannian flow, Ricci-Yamabe map, volume variation, volume entropy