R2和R3中的仿射弹性曲线——概念与方法(英文)
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库存2件
作者黄荣培|责编:张永芹//邵长玲
出版社哈尔滨工业大学
ISBN9787576702798
出版时间2022-08
装帧平装
开本其他
定价38元
货号31738288
上书时间2024-10-12
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该书致力于研究在R2和R3中的中心仿射变换或等仿射变换下的仿射曲线不变的变分性质。它可以被认为是经典欧几里得弹性曲线研究的对应物。
该书内容以作者在凯斯西储大学的博士学位论文以及作者对该主题的进一步研究为基础。
作者简介黄荣培，华东师范大学助教。2020年，他在凯斯西储大学获得了博士学位。他的研究方向是几何学，特别是黎曼几何、积分几何和变分问题。
目录
1 Introduction
1.1 Background of elastica theory
1.2 The goal of this book
1.3 A brief review of the classical elastica in three-dimensionalEuclidean space E3
1.4 A simple introduction to elliptic functions and elliptic equations 13
1.5 Some basic concepts of affine space
2 The Centroaffine elastica in the affine plane R2
2.1 Definition and variation formula of the generalized centroaffineelastica in R2
2.2 Integration of the generalized centroaffine elastica in R2
2.3 Centro-affine elastica for p(k) = k2 + X in the affine plane R2
2.3.1 The solutions of motion equation for centroaffine elastica
2.3.2 The solutions of the structure equation for centroaffine elastica in the affine plane R2
2.3.3 Closed centroaffine elastica
2.3.4 Second variation formula
3 Centroaffine elastica in affine space R3
3.1 Definition and variation formula of the energy functional in R3 59
3.2 Integration of the generalized centroaffine elastica in R3
3.3 Centroaffine elastica for p(k) = k2 + A in the affine space R3
3.3.1 Motion equation of the centroaffine elastica
3.3.2 Solutions of the centroaffine elastica
3.3.3 Closed centroaffine elastica
3.4 The variation of centroaffine torsion for Starlike curves
3.5 Hamiltonian lows on the space of starlike curves in the affine space R3
3.6 Flow Generated by the vector field -k'X+kX'
4 Affine elastica in the affine plane R2
4.1 Definition and variation formula of affine elastica in the affine plane R2
4.2 Affine elastica for p(k) = k2 + X in the affine plane R2
4.2.1 The solutions of motion equation for affine elastica
4.2.2 Second variation of affine elastica in R2
4.3 Critical curves for p(k) = k + > in the affine plane R2
5 Affine elastica in the affine space R3
5.1 Definition and variation formula of the affine elastica in theaffine space R3
5.2 Variation of the energy functional Jx(k2 + A)ds in the affinespace R3
编辑手记
内容摘要
本书致力于研究在R2和R3中的中心仿射变换或等仿射变换下的仿射曲线不变的变分性质。它可以被认为是经典欧几里得弹性曲线研究的对应物。本书内容以作者在凯斯西储大学的博士学位论文以及作者对该主题的进一步研究为基础。
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