The Laplacian Flow of Locally Conformal Calibrated G2-Structures

The Laplacian Flow of Locally Conformal Calibrated G2-Structures

Blog Article

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 006719f 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 ( lime sizzler firebush for sale 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.