ON THE DEFORMATION OF A SURFACE PRESERVING IT IS TOTAL CURVATURE

Abstract: In this paper, we consider a linear transformation from the Heisenberg group of the plane to itself. The transformation matrix is not symmetrical or orthogonal. The geometric invariants of the surface preserved by such transformations on the tangent plane of this surface are studied. It is proved that the total curvature of the surface does not change in this chosen linear transformation.

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