engleski

Transformation of surfaces in the pseudo-Galilean space

Study of surfaces for which a non-trivial relation between their Gaussian and mean curvature holds is a classical problem of Euclidean differential geometry introduced by Julius Weingarten in 1861. As a special case of these surfaces, surfaces of constant Gaussian curvature (CGC) and constant mean curvature (CMC) appear. Moreover, it is well-known fact that surfaces with negative Gaussian curvature can be determined as solutions of Sine-Gordon equation. This equation plays very important role in the soliton theory. In projective-metric spaces the analogous problem can be analyzed. We have treated the problem of Weingarten surfaces in the pseudo-Galilean geometry and obtained results analogous to those in Euclidean geometry concerning surfaces of revolution and ruled surfaces. Moreover, spacelike surfaces with negative Gaussian curvatures are connected to the Klein-Gordon equation. In order to further investigate Weingarten surfaces we have brought in transformation of surfaces in pseudo-Galilean space analogous to Bäcklund transformations in Euclidean geometry.

sine-Gordon equation; Klein-Gordon equation; Galilean geometry

nije evidentirano