Linked from

The 12 pages that link to Ricci curvature, each with the reason it gives.

• Riemann curvature tensorBroader topic: It retains part of the tensor's information while discarding directional detail.

• Christoffel symbolsBroader topic: Its coordinate components can be calculated from the symbols and their derivatives.

• Poincaré conjectureRelated: Ricci curvature determines the direction and rate of change in Ricci flow.

• Tensor calculusBroader topic: It appears in Einstein's field equations and many geometric evolution equations.

• Ricci flowBroader topic: It supplies the curvature term that dictates the metric’s rate of change.

• Grigori PerelmanRelated: Ricci curvature is the geometric quantity driving the flow Hamilton introduced.

• Gregorio Ricci-CurbastroBroader topic: Its contraction of the Riemann curvature tensor illustrates the calculus’s power in geometry.

• Raychaudhuri equationRelated: The Ricci term determines how matter and curvature directly focus the congruence.

• Shing-Tung YauRelated: The Calabi conjecture prescribes the Ricci curvature of a Kähler metric through its volume form.

• Gromov's compactness theoremRelated: Ricci curvature bounds often combine with diameter bounds to control geometric limits.

• Cartan–Hadamard conjectureRelated: It offers a broader curvature condition often used in volume comparison, unlike the conjecture's sectional bound.

• Myers's theoremRelated: The theorem requires a uniform positive lower bound on this curvature.