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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.
Güler et al. (Mon,) studied this question.