An analog of the Gauss–Aleksandrov theorem about the area of the spherical image of a nonconvex polyhedral angle without singularities

Abstract

In this paper, we formulate the definitions of еру spherical image, the area of the spherical image, and the implementation curvature for a class of polyhedral angles without singularities. Also, we prove a theorem on the equality of the area of the spherical image and the implementation curvature of a polyhedral angle from a distinguished class.