Geodesic completeness for type A surfaces

被引：6

作者：

D'Ascanio, D. ^{[1
]}

Gilkey, P. ^{[2
]}

Pisani, P. ^{[1
,3
]}

机构：

[1] Univ Nacl La Plata, CONICET, Inst Fis La Plata, CC 67, RA-1900 La Plata, Buenos Aires, Argentina

[2] Univ Oregon, Dept Math, Eugene, OR 97403 USA

[3] Univ Nacl La Plata, Fac Ciencias Exactas, Dept Fis, CC 67, RA-1900 La Plata, Buenos Aires, Argentina

来源：

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2017年 / 54卷

关键词：

Ricci tensor; Homogeneous affine surface; Geodesic completeness; HOMOGENEOUS AFFINE CONNECTIONS; 2-DIMENSIONAL MANIFOLDS; COMPACT SURFACES; CLASSIFICATION;

D O I：

10.1016/j.difgeo.2016.12.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Type A surfaces are the locally homogeneous affine surfaces which can be locally described by constant Christoffel symbols. We address the issue of the geodesic completeness of these surfaces: we show that some models for Type A surfaces are geodesically complete, that some others admit an incomplete geodesic but model geodesically complete surfaces, and that there are also others which do not model any geodesically complete surface. Our main result provides a way of determining whether a given set of constant Christoffel symbols can model a geodesically complete surface. (c) 2016 Elsevier B.V. All rights reserved.

引用

页码：31 / 43

页数：13

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