We will consider a τ-flow, given by the equation d/dtgij = -2Rij + 1/7tau;gij on a closed manifold M, for all times t ∈ [0, ∞). We will prove that if the curvature operator and the diameter of (M, g(t)) are uniformly bounded along the flow, then we have a sequential convergence of the flow toward the solitons. If we also assume that one of the limit solitons is integrable, then we have a convergence toward a unique soliton, up to a diffeomorphism.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Geometry and Topology
- Statistics, Probability and Uncertainty