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.
Riemannian flow, Ricci-Yamabe map, volume variation, volume entropy
GÜLER, SİNEM and CRASMAREANU, MIRCEA
"Ricci-Yamabe maps for Riemannian flows and their volume variation and volume entropy,"
Turkish Journal of Mathematics: Vol. 43:
5, Article 44.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss5/44