The Laplacian flow of locally conformal calibrated G2-structures

Fernández, M. ; Manero, V. (Universidad de Zaragoza) ; Sánchez, J.

Resumen: We consider the Laplacian flow of locally conformal calibrated G2 -structures as a natural extension to these structures of the well-known Laplacian flow of calibrated G2 -structures. We study the Laplacian flow for two explicit examples of locally conformal calibrated G2 manifolds and, in both cases, we obtain a flow of locally conformal calibrated G2 -structures, which are ancient solutions, that is they are defined on a time interval of the form (−∞,T) , where T>0 is a real number. Moreover, for each of these examples, we prove that the underlying metrics g(t) of the solution converge smoothly, up to pull-back by time-dependent diffeomorphisms, to a flat metric as t goes to −∞ , and they blow-up at a finite-time singularity.

Idioma: Inglés

DOI: 10.3390/axioms8010007

Año: 2019

Publicado en: Axioms 8, 1 (2019), 7 [15 pp]
ISSN: 2075-1680

Factor impacto SCIMAGO: 0.314 - Geometry and Topology (Q3) - Analysis (Q3) - Mathematical Physics (Q3) - Logic (Q3) - Algebra and Number Theory (Q4)

Financiación: info:eu-repo/grantAgreement/ES/DGA/E22-17R
Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2014-54804-P
Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2017-85649-P

Tipo y forma: Article (Published version)

Área (Departamento): Área Didáctica Matemática (Dpto. Matemáticas)