Homogeneous G-structures

被引：1

作者：

Tortorella, Alfonso Giuseppe ^{[1
]}

Vitagliano, Luca ^{[2
]}

Yudilevich, Ori ^{[1
]}

机构：

[1] Katholieke Univ Leuven, Dept Math, Celestijnenlaan 200B, B-3001 Leuven, Belgium

[2] Univ Salerno, DipMat, Via Giovanni Paolo II 123, I-84084 Fisciano, SA, Italy

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2020年 / 199卷 / 06期

关键词：

G-structures; Contact structures; Atiyah algebroid;

D O I：

10.1007/s10231-020-00972-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The theory of G-structures provides us with a unified framework for a large class of geometric structures, including symplectic, complex and Riemannian structures, as well as foliations and many others. Surprisingly, contact geometry-the "odd-dimensional counterpart" of symplectic geometry-does not fit naturally into this picture. In this paper, we introduce the notion of a homogeneous G-structure, which encompasses contact structures, as well as some other interesting examples that appear in the literature.

引用

页码：2357 / 2380

页数：24

共 15 条

[1] [Anonymous], 1984, SER PURE MATH
[2] Blair D. E., 2002, Progress in Mathematics, V203
[3] Remarks on Contact and Jacobi Geometry
Bruce, Andrew James
Grabowska, Katarzyna
Grabowski, Janusz
[J]. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2017, 13
[4] A SURVEY ON COSYMPLECTIC GEOMETRY
Cappelletti-Montano, Beniamino
De Nicola, Antonio
Yudin, Ivan
[J]. REVIEWS IN MATHEMATICAL PHYSICS, 2013, 25 (10)
[5] Crainic M, 2015, LECT NOTES
[6] Geiges H, 2008, CAMBRIDGE STUD ADV M, V109
[7] SOME GLOBAL PROPERTIES OF CONTACT STRUCTURES
GRAY, JW
[J]. ANNALS OF MATHEMATICS, 1959, 69 (02) : 421 - 450
[8] Symplectic and Poisson geometry on b-manifolds
Guillemin, Victor
Miranda, Eva
Pires, Ana Rita
[J]. ADVANCES IN MATHEMATICS, 2014, 264 : 864 - 896
[9] Kobayashi S., 1972, Transformation Groups in Differential Geometry
[10] Mackenzie K., 2005, GEN THEORY LIE GROUP

← 1 2 →