On the geometry of spaces of oriented geodesics

被引：22

作者：

Alekseevsky, Dmitri V. ^{[2
,3
]}

Guilfoyle, Brendan ^{[1
]}

Klingenberg, Wilhelm ^{[4
]}

机构：

[1] IT Tralee, Dept Comp & Math, Clash, Tralee County K, Ireland

[2] Univ Edinburgh, Sch Math, Edinburgh EH9 3JZ, Midlothian, Scotland

[3] Univ Edinburgh, Maxwell Insitute Math Sci, JCMB, Edinburgh EH9 3JZ, Midlothian, Scotland

[4] Univ Durham, Sch Math Sci, Durham DH1 3LE, England

来源：

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2011年 / 40卷 / 04期

关键词：

Space of geodesics; Homogeneous manifolds; Pseudo-Riemannian metrics; Symplectic structures; Kahler structures; LINES;

D O I：

10.1007/s10455-011-9261-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let M be either a simply connected pseudo-Riemannian space of constant curvature or a rank one Riemannian symmetric space, and consider the space L(M) of oriented geodesics of M. The space L(M) is a smooth homogeneous manifold and in this paper we describe all invariant symplectic structures, (para)complex structures, pseudo-Riemannian metrics and (para)Kahler structure on L(M).

引用

页码：389 / 409

页数：21

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