The Laplacian Flow of Locally Conformal Calibrated G2-Structures
Departamento de Matemáticas, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain
Departamento de Matemáticas—IUMA, Facultad de Ciencias Humanas y de la Educación, Universidad de Zaragoza, 22003 Huesca, Spain
Author to whom correspondence should be addressed.
Received: 8 November 2018 / Revised: 31 December 2018 / Accepted: 3 January 2019 / Published: 11 January 2019
We consider the Laplacian flow of locally conformal calibrated
-structures as a natural extension to these structures of the well-known Laplacian flow of calibrated
-structures. We study the Laplacian flow for two explicit examples of locally conformal calibrated
manifolds and, in both cases, we obtain a flow of locally conformal calibrated
-structures, which are ancient solutions, that is they are defined on a time interval of the form
is a real number. Moreover, for each of these examples, we prove that the underlying metrics
of the solution converge smoothly, up to pull-back by time-dependent diffeomorphisms, to a flat metric as t
, and they blow-up at a finite-time singularity.
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MDPI and ACS Style
Fernández, M.; Manero, V.; Sánchez, J. The Laplacian Flow of Locally Conformal Calibrated G2-Structures. Axioms 2019, 8, 7.
Fernández M, Manero V, Sánchez J. The Laplacian Flow of Locally Conformal Calibrated G2-Structures. Axioms. 2019; 8(1):7.
Fernández, Marisa; Manero, Victor; Sánchez, Jonatan. 2019. "The Laplacian Flow of Locally Conformal Calibrated G2-Structures." Axioms 8, no. 1: 7.
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