Ansatze are constructed under which the solutions of 11-dimensional 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 11-dimensional supergravity. As a first step, Shi-type estimates and criteria for the long-time existence of the flow are established.
All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Applied Mathematics
- 11-dimensional supergravity
- Shi-type estimates