๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Motion of surfaces in 3-dimensional space

โœ Scribed by Kazuaki Nakayama; Miki Wadati

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
798 KB
Volume
37
Category
Article
ISSN
0378-4754

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โœฆ Synopsis

Kinematics

of surfaces in 3-dimensional space is formulated in terms of the differential geometry. The formulation is intrinsic and the surface is described by its metric and curvature tensors. It is found that the introduction of nontrivial time evolution of coordinate system makes the theory transparent. Applications to some surfaces, which are paremetrized by the lines of curvature, are presented. As a concrete example, I-soliton solution of the zero-curvature surfaces is obtained.

๐Ÿ“œ SIMILAR VOLUMES

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โœ Juan A. Aledo; Alfonso Romero ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 127 KB

In this paper, we establish several sufficient conditions for a compact spacelike surface with non-degenerate second fundamental form in the 3-dimensional de Sitter space to be spherical. With this aim, we develop a formula for these surfaces which involves the mean and Gaussian curvatures of the fi

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The aim of the present paper is to clarify the relationship between immersions of surfaces and solutions of the Dirac equation. The main idea leading to the description of a surface M2 by a spinor field is the observation that the restriction to M2 of any parallel spinor $ on Iw3 is a non-trivial sp