Abstract
In a previous paper [4] the present author studied a C ∞ mapping \(\tilde x:M \times I \to R^n\)where M is an m-dimensional C ∞ manifold, I is some interval and for each t∈I the mapping \(\tilde x_t :M \times I \to R^n\)is an immersion satisfying the following conditions, (i) The Gauss map associated with the immersion is regular. (ii) The Gauss image of the immersed submanifold is fixed against t for each point p of M. Such a mapping \(\tilde x\) was called an admissible deformation. The purpose of the present paper is to give results obtained since then.
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References
Ferus, D., ‘Produkt-Zerlegung von Immersionen mit paralleler zweiter Fundamental-form’. Math. Ann. 211 (1974), 1–5.
Moore, J. D., ‘Isometric Immersions of Riemannian products’. J. Differential Geo. 5 (1971), 159–168.
Mutō, Y., ‘The Gauss Map of a Submanifold in a Euclidean Space’. J. Math. Soc. Japan 30 (1978), 85–100.
Mutō, Y., ‘Deformability of a Submanifold in a Euclidean Space whose Image by the Gauss Map is Fixed’. Proc. Amer. Math. Soc., 76 (1979), 140–144.
Walden, R., ‘Untermannigfaltigkeiten mit paralleler zweiter Fundamentalform in Euklidischen Räumen und Sphären’. Manuscripta Math. 10 (1973), 91–102.
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Mutō, Y. Deformation of a submanifold in an Euclidean space with fixed Gauss image. Geom Dedicata 11, 1–18 (1981). https://doi.org/10.1007/BF00183186
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DOI: https://doi.org/10.1007/BF00183186