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-  2019 

The Laplacian Flow of Locally Conformal Calibrated G2-Structures

DOI: https://doi.org/10.3390/axioms8010007

Keywords: locally conformal calibrated G2-structures, Laplacian flow, solvable Lie algebras

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Abstract:

Abstract We consider the Laplacian flow of locally conformal calibrated G 2 -structures as a natural extension to these structures of the well-known Laplacian flow of calibrated G 2 -structures. We study the Laplacian flow for two explicit examples of locally conformal calibrated G 2 manifolds and, in both cases, we obtain a flow of locally conformal calibrated G 2 -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. View Full-Tex

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