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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Deformability of a submanifold in a Euclidean space whose image by the Gauss map is fixed

Author: Yosio Muto
Journal: Proc. Amer. Math. Soc. 76 (1979), 140-144
MSC: Primary 53B25
MathSciNet review: 534405
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Abstract: In the present paper, deformations of an immersion of an m-dimensional manifold M in Euclidean n-space $ {R^n}$ 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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PII: S 0002-9939(1979)0534405-4
Keywords: Submanifold of Euclidean space, deformation with fixed Gauss image, admissible deformation
Article copyright: © Copyright 1979 American Mathematical Society