Geodesics in Static Lorentzian Manifolds with Critical Quadratic Behavior

Author:

Bartolo R.1,Candela A.M.2,Flores J.L.3,Sánchez M.3

Affiliation:

1. Dipartimento di Matematica, Politecnico di Bari Via G. Amendola 126/B, 70126 Bari, Italy

2. Dipartimento di Matematica, Università degli Studi di Bari Via E. Orabona 4, 70125 Bari, Italy

3. Departamento de Geometría y Topología Facultad de Ciencias, Universidad de Granada Auenida Fuentenueva s/n, 18071 Granada, Spain

Abstract

Abstract The aim of this paper is t o study the geodesic connectedness of a complete static Lorentzian manifold (M.〈·, ·〉L) such that. if K is its irrotational timelike Killing vector field, the growth of β = -〈K, K〉L is (at most) quadratic. This is shown to be equivalent to a critical variational problem on a Riemannian manifold, where some geometrical interpretations yield the optimal results. Multiplicity of connecting geodesics is studied, especially in the timelike case, where the restrictions for the number of causal connecting geodesics are stressed. Extensions to the non-complete case, including discussions on pseudoconvexity, are also given.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Cited by 10 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Global Geodesic Properties of Gödel-type SpaceTimes;Recent Trends in Lorentzian Geometry;2012

2. A note on geodesic connectedness of Gödel type spacetimes;Differential Geometry and its Applications;2011-12

3. Lightlike rays in stationary spacetimes with critical growth;Nonlinear Analysis: Theory, Methods & Applications;2008-07

4. Global hyperbolicity and Palais–Smale condition for action functionals in stationary spacetimes;Advances in Mathematics;2008-06

5. Geodesic connectedness of stationary spacetimes with optimal growth;Journal of Geometry and Physics;2006-10

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3