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What (who) is P-curvature - definition
P-curvature
In algebraic geometry, -curvature is an invariant of a connection on a coherent sheaf for schemes of characteristic . It is a construction similar to a usual curvature, but only exists in finite characteristic.
Grothendieck–Katz p-curvature conjecture
In mathematics, the Grothendieck–Katz p-curvature conjecture is a local-global principle for linear ordinary differential equations, related to differential Galois theory and in a loose sense analogous to the result in the Chebotarev density theorem considered as the polynomial case. It is a conjecture of Alexander Grothendieck from the late 1960s, and apparently not published by him in any form.
Ricci curvature
2-TENSOR OBTAINED AS A CONTRACTION OF THE RIEMAN CURVATURE 4-TENSOR ON A RIEMANNIAN MANIFOLD (OR, MORE GENERALLY, A SMOOTH MANIFOLD EQUIPPED WITH AFFINE CONNECTION)
Ricci-curvature; Ricci curvature tensor; Ricci tensor; Trace-free Ricci tensor; Ricci form; Ricci Curvature
In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian or pseudo-Riemannian metric on a manifold. It can be considered, broadly, as a measure of the degree to which the geometry of a given metric tensor differs locally from that of ordinary Euclidean space or pseudo-Euclidean space.
