Physical and Mathematical Sciences | Article | Published 2022-10-14

PROPERTIES OF A DUAL SURFACE IN A MULTIDIMENSIONAL ISOTROPIC SPACE

Authors:
Publisher: Physical and Mathematical
Collection: Physical and Mathematical sciences
DOI: 10.5281/zenodo.7198959
Keywords: an isotropic space, Gallеan plane, isotropic sphere, first and second fundamental form, dual map, dual surface, Legendre transformations.

Abstract

In the paper, we define an isotropic sphere in a multidimensional isotropic space, which is affine to be a paraboloid of rotation. We show the method that compares a point of the dual image to a plane to any hyperplane intersecting an isotropic sphere. It is determined the dual sphere to the surface contained within an isotropic sphere. It is studied the connection between the total curvatures of the surface and its dual image. We prove that the dual image of the dual surface coincides with the surface.

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