Oscillator spacetimes are Ricci solitons. (July 2016)

• Record Type: Journal Article
• Authors: Calvaruso, Giovanni
• Is Part Of: Nonlinear analysis. Volume 140(2016)
• Page Start: 254
• Page End: 269
• Publication Date: 2016-07
• Subjects: 53C50 -- 53B30 -- 35A01; Oscillator group -- Ricci solitons -- Yamabe solitons; 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.2016.03.008
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider the four-dimensional oscillator group, equipped with a well-known one-parameter family of left-invariant Lorentzian metrics, which includes the bi-invariant one (Gadea & Oubiña, 1999). In a suitable system of global coordinates, the Ricci soliton equation for these metrics translates into a system of partial differential equations. Solving such system, we prove that all these metrics are Ricci solitons. In particular, the bi-invariant metric on the oscillator group gives rise to infinitely many Ricci solitons (and so, also to Yamabe solitons).