R2和R3中的仿射彈性曲線-概念與方法 (英文) 黃榮培 9787576702798 【台灣高等教育出版社】

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書名：R2和R3中的仿射彈性曲線-概念與方法 (英文)
ISBN：9787576702798
出版社：哈爾濱工業大學
著編譯者：黃榮培
叢書名：國外優秀數學著作原版系列
頁數：267
所在地：中國大陸 *此為代購商品
書號：1527418
可大量預訂，請先連絡。

內容簡介

本書致力於研究在R2和R3中的中心仿射變換或等仿射變換下的仿射曲線不變的變分性質。它可以被認為是經典歐幾里得彈性曲線研究的對應物。本書內容以作者在凱斯西儲大學的博士學位論文以及作者對該主題的進一步研究為基礎。

作者簡介

黃榮培，華東師範大學助教。2020年，他在凱斯西儲大學獲得了博士學位。他的研究方向是幾何學，特別是黎曼幾何、積分幾何和變分問題。

目錄

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
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