This article is cited in 2 papers

MATHEMATICS

Minimal non-holonomic torses of the sekond kind

N. M. Onishchuk, O. V. Tsokolova

Tomsk State University, Faculty of Mechanics and Mathematics

Abstract: We consider non-holonomic smooth two-dimensional distributions of planes with zero mean curvature and zero total curvature of the second kind in the three- dimensional Euclidean space $E_3$. They are called minimal non-holonomic torses of the second kind ($MNT-2$). We prove that there exist three types of $MNT-2$ and study geometric properties of all these types.

Keywords: non-holonomic geometry, distribution of planes, Pfaffian equation, vector field.

UDC: 514.752


Accepted: May 19, 2009