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


Boskoff, Wladimir G., Crâsmăreanu, Mircea and Pişcoran, Laurian Ioan


Abstract

carpathian_2017_33_2_141_151_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.

Additional Information

Author(s)

Boskoff, Wladimir G, Crâșmăreanu, Mircea, Pişcoran, Laurian-Ioan