Ansatze are constructed under which the solutions of 11D supergravity must be stationary points of a parabolic flow on a Riemannian manifold $M^{ 10-p}$. This parabolic flow turns out to be the Ricci flow coupled to a scalar field, a $(3-p)$-form, and a $4$-form. This allows the introduction of techniques from parabolic partial differential equations to the search of solutions to 11D supergravity. As a first step, Shi-type estimates and criteria for the long-time existence of the flow are established.
Categories: math.DG hep-th math-ph math.AP math.MP
