Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 1003–1011

REDUCTION OF GRADIENT RICCI SOLITON EQUATION

Benedito Leandro and João Paulo dos Santos

Universidade Federal de Goiás, Instituto de Matemática e Estatística
Goiânia, 74001-970, Brazil; bleandroneto 'at' ufg.br

Universidade de Brasília, Departmento de Matemática
70910-900, Brasília-DF, Brazil; joaopsantos 'at' unb.br

Abstract. We consider gradient Ricci solitons conformal to an $n$-dimensional pseudo-Euclidean space and we describe entirely the most general substitution that reduces the resulting system of partial differential equations, originated from the gradient Ricci soliton equations, to a system of ordinary differential equations. As a consequence, the gradient Ricci solitons that arise from the reduced system are invariant under the action of either an (n – 1)-dimensional translation group or the pseudo-orthogonal group acting on the corresponding $n$-dimensional pseudo-Euclidean space. The reduced system of ordinary differential equations is given. From such a system, particular solutions are obtained.

2010 Mathematics Subject Classification: Primary 53C21, 53C50, 53C44.

Key words: Gradient Ricci solitons, exact solutions, reduction, conformal metrics.

Reference to this article: B. Leandro and J. P. dos Santos: Reduction of gradient Ricci soliton equations. Ann. Acad. Sci. Fenn. Math. 45 (2020), 1003–1011.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4554