Agradecimentos: The authors would like to thank Simon Salamon, Mark Haskins and Andrés Moreno for some valuable discussions. JL and HSE were supported by a UK Royal Society Newton Mobility Award [NMG\R1\191068]. JL is also partially supported by the Simons Collaboration on Special Holonomy in Geometry, Analysis, and Physics (#724071 Jason Lotay). HSE has also been supported by the São Paulo Research Foundation (Fapesp) [2018/21391-1] and the Brazilian National Council for Scientific and Technological Development (CNPq) [311128/2020-3]. JPS was supported by the Coordination for the Improvement of Higher Education Personnel-Brazil (CAPES) [88882.329037/2019-1] Ver menos

Abstract: We study the Laplacian flow and coflow on contact Calabi-Yau 7-manifolds. We show that the natural initial condition leads to an ancient solution of the Laplacian flow with a finite time Type I singularity which is not a soliton, whereas it produces an immortal (though neither eternal nor self-similar) solution of the Laplacian coflow which has an infinite time singularity of Type IIb, unless the transverse Calabi-Yau geometry is flat. The flows in each case collapse (under normalised volume) to a lower-dimensional limit, which is either R, for the Laplacian flow, or standard C-3, for the Laplacian coflow. We also study the Hitchin flow in this setting, which we show coincides with the Laplacian coflow, up to reparametrisation of time, and defines an (incomplete) Calabi-Yau structure on the spacetime track of the flow Ver menos