Conformal geometry of timelike curves in the (1+2)-Einstein universe. (September 2016)

• Record Type: Journal Article
• Authors: Dzhalilov, Akhtam; Musso, Emilio; Nicolodi, Lorenzo
• Is Part Of: Nonlinear analysis. Volume 143(2016)
• Page Start: 224
• Page End: 255
• Publication Date: 2016-09
• Subjects: 53C50 -- 53A30; Conformal Lorentzian geometry -- Timelike curves -- Closed timelike curves -- Conformal invariants -- Einstein universe -- Conformal Lorentzian compactification -- Conformal strain functional; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.05.011
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the conformal geometry of timelike curves in the ( 1 + 2 ) -Einstein universe, the conformal compactification of Minkowski 3-space defined as the quotient of the null cone of R 2, 3 by the action by positive scalar multiplications. The purpose is to describe local and global conformal invariants of timelike curves and to address the question of existence and properties of closed trajectories for the conformal strain functional. Some relations between the conformal geometry of timelike curves and the geometry of knots and links in the 3-sphere are discussed.