Representation for a Smooth Isometric Mapping from a Connected Planar Domain to a Surface
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- 作者：Yi-Chao Chen (1)
Roger Fosdick (2)
Eliot Fried (3)
1. Department of Mechanical Engineering ; University of Houston ; Houston ; TX ; 77204-4006 ; USA
2. Department of Aerospace Engineering and Mechanics ; University of Minnesota ; Minneapolis ; MN ; 55455-0153 ; USA
3. Mathematical Soft Matter Unit ; Okinawa Institute of Science and Technology Graduate University ; Onna ; Okinawa ; 904-0495 ; Japan - 关键词：Isometric embedding ; Rigidity ; Representation theorem ; 2 ; d to 3 ; d ; 53A05 ; 74K15 ; 74K35 ; 57R40 ; 53A45
- 刊名：Journal of Elasticity
- 出版年：2015
- 出版时间：April 2015
- 年：2015
- 卷：119
- 期：1-2
- 页码：335-350
- 全文大小：743 KB
- 刊物类别：Physics and Astronomy
- 刊物主题：Physics
Mechanics
Automotive and Aerospace Engineering and Traffic - 出版者：Springer Netherlands
- ISSN：1573-2681
文摘
A representation theorem for a smooth isometric mapping of a flat, connected domain \(\mathcal {D}\) in two-dimensional Euclidean point space \(\mathcal {E}^{2}\) into a surface \(\mathcal {S}\) in three-dimensional Euclidean point space \(\mathcal {E}^{3}\) is presented. The form of the mapping is shown to be necessary and sufficient to describe any such smooth isometry. Importantly, this work is not based upon the hypothesis that the mapped surface is ruled. In general, a mapping from a flat planar domain into a ruled surface is far from being isometric, and the property of being ruled is a partial consequence of our representation theorem.