Results 181 to 190 of about 1,504 (198)

Isometric approximation property in euclidean spaces

Israel Journal of Mathematics, 2002
The paper is concerned with \( \varepsilon\)-nearisometries \(f: A \rightarrow {\mathbb R}^n\) where \(f\) satisfies \[ | x-y| - \varepsilon \leq | f(x)-f(y) | \leq | x-y| + \varepsilon, \quad x, y \in A. \] The question is discussed whether an \( \varepsilon\)-nearisometry is always a perturbation of an isometry: For \( c \geq 1\), the set \(A\) has ...
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On isometric immersion of nilmanifolds in Euclidean space

Mathematical Notes, 2010
[2].However, this result can be strengthened; moreover, it can be extended to nilpotent groups of nilpotencyclass 2, and in the cases where such a group admits a locally isometric immersion in Euclidean space,the codimension of the immersion can be estimated.
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Isometric immersions of Euclidean plane into Euclidean 4-space with vanishing normal curvature

Tohoku Mathematical Journal, 2009
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Mori, Hiroshi, Shimakura, Norio
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Isometric Representations of Non-Euclidean Spaces within Euclidean Spaces

                                                        Abstract We present a geometric and informational interpretation of the classical problem concerningthe isometric representation of a ν-dimensional Riemannian manifold within a Euclidean space ofsufficiently high dimension.
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ISOMETRIC IMMERSIONS OF TWO-DIMENSIONAL RIEMANNIAN METRICS IN EUCLIDEAN SPACE

Russian Mathematical Surveys, 1973
In this paper we consider the problem of global isometric immersions of two-dimensional Riemannian metrics in Euclidean space. The dimension of the ambient space depends on the character of the Riemannian metric in question.
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Equations of isometric imbeddings in three-dimensional Euclidean space of two-dimensional manifolds of negative curvature

Mathematical Notes, 1982
E V Shikin, Shikin E V
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Isometric submanifolds of arbitrary codimension in Euclidean space with the same Grassman image

Mathematical Notes, 1992
Borisenko A A
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Isometric Deformation of (m,n)-Type Helicoidal Surface in the Three Dimensional Euclidean Space

Mathematics, 2018
Erhan GÜLER, GÜLER Erhan
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Isometric Immersions of Lobachevski Space into Euclidean Space

2001
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The space of smooth isometric immersions of a compact manifold into an Euclidean space is a Fréchet manifold

1984
Let M be a compact connected smooth manifold, \(I(M,{\mathbb{R}}^ n)\) the set of all smooth immersions of M into \({\mathbb{R}}^ n\) and, for each \(i\in I(M,R^ n)\), let \(O_ i\) be the (connected) component of \(I(M,R^ n)(\subset C^{\infty}(M,R)\) with Whitney's \(C^{\infty}\)-topology) containing i.
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