Differential Geometry of Moving Surfaces and its Relations to Solitons

Andrei Ludu

doi:10.7546/jgsp-21-2011-1-28

Differential Geometry of Moving Surfaces and its Relations to Solitons

Andrei Ludu

Northwestern State University, Louisiana

Research output: Contribution to journal › Article › peer-review

Abstract

In this article we present an introduction in the geometrical theory of motion of curves and surfaces in R3, and its relations with the nonlinear integrable systems. The working frame is the Cartan's theory of moving frames together with Cartan connection. The formalism for the motion of curves is constructed in the Serret-Frenet frames as elements of the bundle of adapted frames. The motion of surfaces is investigated in the Gauss-Weingarten frame. We present the relations between types of motions and nonlinear equations and their soliton solutions.

Original language	American English
Journal	Journal of Geometry and Symmetry in Physics
Volume	21
DOIs	https://doi.org/10.7546/jgsp-21-2011-1-28
State	Published - 2011
Externally published	Yes

Keywords

differential geometry
moving surface
Cartan connection
integrable forms
moving frames
Serret-Frenet
Gauss-Weingarten

Disciplines

Geometry and Topology
Physics

Access to Document

10.7546/jgsp-21-2011-1-28License: Unspecified

Cite this

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abstract = " In this article we present an introduction in the geometrical theory of motion of curves and surfaces in R3, and its relations with the nonlinear integrable systems. The working frame is the Cartan's theory of moving frames together with Cartan connection. The formalism for the motion of curves is constructed in the Serret-Frenet frames as elements of the bundle of adapted frames. The motion of surfaces is investigated in the Gauss-Weingarten frame. We present the relations between types of motions and nonlinear equations and their soliton solutions.",

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AB - In this article we present an introduction in the geometrical theory of motion of curves and surfaces in R3, and its relations with the nonlinear integrable systems. The working frame is the Cartan's theory of moving frames together with Cartan connection. The formalism for the motion of curves is constructed in the Serret-Frenet frames as elements of the bundle of adapted frames. The motion of surfaces is investigated in the Gauss-Weingarten frame. We present the relations between types of motions and nonlinear equations and their soliton solutions.

KW - differential geometry

KW - moving surface

KW - Cartan connection

KW - integrable forms

KW - moving frames

KW - Serret-Frenet

KW - Gauss-Weingarten

U2 - 10.7546/jgsp-21-2011-1-28

DO - 10.7546/jgsp-21-2011-1-28

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SN - 1314-5673

VL - 21

JO - Journal of Geometry and Symmetry in Physics

JF - Journal of Geometry and Symmetry in Physics

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