2026/07/25 by Daniel Fadel, Udhav Fowdar, Eric Loubeau +2
#math.DG #math.AP
We advance the general theory of flows of tensorial H-structures, focusing on non-isometric flows and on the case H=SU(m)\subsetSO(2m). After developing the relevant SU(m) algebra, we compare two natural evolutions: the unrestricted negative gradient flow of the intrinsic-torsion energy and a Ricci-harmonic flow. We prove short-time existence and uniqueness for the Ricci-harmonic H-flow, with arbitrary lower-order torsion-quadratic terms, for every closed subgroup H\subsetSO(n). For groups for which the projection to \mathfrakh^⊥ defines a 4-form, including \1\, SU(2), G2, and Spin(7), we express the negative gradient flow in Ricci-harmonic form up to explicit lower-order torsion terms and prove short-time existence and uniqueness by a modified DeTurck argument. We treat the genuinely different SU(m) case by a separate principal-symbol computation, proving short-time existence and uniqueness for the unrestricted negative gradient flow of SU(m)-structures. The same computation identifies the natural negative gradient flow of U(m)-structures as a borderline case, which cannot be made strictly parabolic by first-order diffeomorphism gauges. For the modified Ricci-harmonic flow, we derive heat-type evolution equations for the intrinsic torsion, a doubling-time estimate and Shi-type derivative estimates for (|Rm|2+|∇ T|2+|T|4)1/2, and a finite-time continuation criterion. In dimension six, we translate the formalism into the standard torsion forms of an SU(3)-structure and describe, to highest order, the corresponding family of second-order quasilinear SU(3)-flows.