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

Muto, Yosio

doi:10.1090/S0002-9939-1979-0534405-4

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Deformability of a submanifold in a Euclidean space whose image by the Gauss map is fixed
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Proc. Amer. Math. Soc. 76 (1979), 140-144 Request permission

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.

References

Yosio Muto, Submanifolds of a Euclidean space with homothetic Gauss map, J. Math. Soc. Japan 32 (1980), no. 3, 531–555. MR 575405, DOI 10.2969/jmsj/03230531