Invariant Geometric Characteristics Under the Dual Mapping of an Isotropic Space
Шерзодбек ИсмоиловDepartment of Geometry and Topology, National University of Uzbekistan, Tashkent, UzbekistanBekzod SultanovDepartment of Applied mathematics and mathematical physics, Urganch State University, Khorezm, Uzbekistan
ABI
Abstract
A. In the paper, we give the definitions, basic concepts, and formulas of the basic geometric characteristics associated with the surface of an isotropic space R 2 3 .The geometric sense of the dual mapping is revealed.Using the geometric interpretation of the dual mapping, we prove that the dual asymptotic mapping is asymptotic.Some properties of shortest curves on a surface are defined and proved.The geodesicity and conformality of the dual mapping is proved.