Special Mean and Total Curvature of a Dual Surface in Isotropic Spaces

The study of the geometry surfaces in spaces with a degenerate metric is one of the urgent problems of modern geometry since its results find numerous applications in problems of mechanics and quantum mechanics.In this paper, we study the properties of the total and mean curvatures of a surface and its dual image in an isotropic space. We prove the equality of the mean curvature and the second quadratic forms. The relation of the mean curvature of a surface to its dual surface is found. The superimposed space method is used to investigate the geometric characteristics of a surface relative to the normal and special normal.

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