Tzitzeica equations and Tzitzeica surfaces in separable coordinate systems and the Ricci flow tensor field

Abstract

The Tzitzeica equation and two well-known Tzitzeica surfaces are studied in the separable coordinate systems on the plane and space respectively. We study also Tzitzeica graphs with a parameter and interpret the induced class of first fundamental forms as a Riemannian flow. Consequently, we introduce a tensor field which measures how far is a given Riemannian flow to be a Ricci one. This tensor field is explicitly computed for the case of a initial isothermic metric and a flow of convex type.