The origins of the fundamental theorem of surface theory

被引：1

作者：

Cogliati, Alberto ^{[1
]}

Rivis, Rachele ^{[2
]}

机构：

[1] Univ Pisa, Dipartimento Matemat, Largo Bruno Pontecorvo 5, I-56127 Pisa, Italy

[2] Univ Milan, Dipartimento Matemat, Via Cesare Saldini 50, I-20133 Milan, Italy

来源：

HISTORIA MATHEMATICA | 2022年 / 61卷

关键词：

Surface theory; Applicability problem; Fundamental theorem of surface theory; Mainardi-Codazzi equations;

D O I：

10.1016/j.hm.2022.09.001

中图分类号：

N09 [自然科学史]; B [哲学、宗教];

学科分类号：

01 ; 0101 ; 010108 ; 060207 ; 060305 ; 0712 ;

摘要：

The Mainardi-Codazzi equations (MCE) and the fundamental theorem of surface theory (FT) are regarded as crucial achieve-ments in the development of surface theory. The paper offers an analysis of three papers by Bour, Codazzi and Bonnet, submitted on the occasion of the Grand Prix des Mathematiques (1859), in which the MCE and the FT were systematically employed to deal with applicability problems. Our analysis provides a new insight into the historical process leading to a recognition of the relevance of the MCE and the FT and helps explaining why previous contributions on the subject could go unnoticed for years.(c) 2022 Elsevier Inc. All rights reserved.

引用

页码：45 / 79

页数：35

共 50 条

[21] THE FUNDAMENTAL THEOREM IN AFFINE HYPERSURFACE THEORY
SIMON, U
GEOMETRIAE DEDICATA, 1988, 26 (02) : 125 - 137
[22] Fundamental theorem of abelian funcion theory
Painleve, Paul
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES, 1902, 134 : 808 - 813
[23] THE FUNDAMENTAL GROUP OF A SURFACE, AND A THEOREM OF SCHREIER
GRIFFITHS, HB
ACTA MATHEMATICA, 1963, 110 (1-2) : 1 - 17
[24] FUNDAMENTAL THEOREM FOR LAPLACE SURFACE HARMONICS
MCDONALD, KL
BULLETIN OF THE AMERICAN PHYSICAL SOCIETY, 1977, 22 (10): : 1284 - 1284
[25] Optimal Regularity for Two-Dimensional Pfaffian Systems and the Fundamental Theorem of Surface Theory
Litzinger, Florian
JOURNAL OF GEOMETRIC ANALYSIS, 2021, 31 (03) : 2594 - 2610
[26] Optimal Regularity for Two-Dimensional Pfaffian Systems and the Fundamental Theorem of Surface Theory
Florian Litzinger
The Journal of Geometric Analysis, 2021, 31 : 2594 - 2610
[27] STOCHASTIC ANALOGUE OF FUNDAMENTAL THEOREM OF SURFACE THEORY FOR SURFACES OF BOUNDED DISTORTION AND POSITIVE CURVATURE
Klimentov, D. S.
UFA MATHEMATICAL JOURNAL, 2019, 11 (04): : 40 - 48
[28] On the fundamental theorem in the theory of functions of a complex variable
Young, WH
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1912, 10 : 1 - 6
[29] ANOTHER PROOF OF FUNDAMENTAL THEOREM OF GALOIS THEORY
DEMEYER, F
AMERICAN MATHEMATICAL MONTHLY, 1968, 75 (07): : 720 - &
[30] A fundamental theorem in the theory of ruled surfaces.
Wilczynski, EJ
MATHEMATISCHE ANNALEN, 1904, 58 : 249 - 256

← 1 2 3 4 5 →