Heat Flow of Isometric G2-structures

Sergey Grigorian, University of Texas -- Rio Grande Valley

Given a 7-dimensional Riemannian manifold (M,g) that admits G2-structures, all the G2-structures that are compatible with the metric g are parametrized by unit sections of an octonion bundle over M. We define a natural energy functional on unit octonion sections and consider its associated heat flow. The critical points of this functional and flow precisely correspond to G2-structures with divergence-free torsion. In this talk, we will discuss various properties of this flow including derivative estimates, monotonicity, epsilon-regularity, and behavior in the presence of a torsion-free G2-structure.

MC 5403