Deformability of a submanifold in a Euclidean space whose image by the Gauss map is fixed
Abstract: In the present paper, deformations of an immersion of an m-dimensional manifold M in Euclidean n-space such that the Gauss image is fixed pointwise are studied. We call such deformations admissible deformations. The main theorem gives a necessary and sufficient condition for an immersed manifold to admit nontrivial admissible deformations.
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Keywords: Submanifold of Euclidean space, deformation with fixed Gauss image, admissible deformation
Article copyright: © Copyright 1979 American Mathematical Society