Estimating the trace-free Ricci tensor in Ricci flow

Ricci Lower Bound for Kähler–ricci Flow

Curvature Tensor under the Complete Non-compact Ricci Flow

We prove that for a solution (M, g(t)), t ∈ [0, T ), where T < ∞, to the Ricci flow on a complete non-compact Riemannian manifold with the Ricci curvature tensor uniformly bounded by some constant C on M × [0, T ), the curvature tensor stays uniformly bounded on M × [0, T ).

Positivity of Ricci Curvature under the Kähler–ricci Flow

An invariant cone in the space of curvature operators is one that is preserved by a flow. For Ricci flow, the condition R ≥ 0 is preserved in all dimensions, while the conditionR ≤ 0 is preserved only in real dimension two. Positive curvature operator is preserved in all dimensions [11], but positive sectional curvature is not preserved in dimensions four and above. The known counterexamples, c...

Ricci Tensor of Diagonal Metric

Efficient formulae of Ricci tensor for an arbitrary diagonal metric are presented.

Ricci Flow Gravity

A theory of gravitation is proposed, modeled after the notion of a Ricci flow. In addition to the metric an independent volume enters as a fundamental geometric structure. Einstein gravity is included as a limiting case. Despite being a scalar-tensor theory the coupling to matter is different from Jordan-Brans-Dicke gravity. In particular there is no adjustable coupling constant. For the solar ...