Multivectorial Curvature

Multivectorial abnormal cell migration in the NOD mouse thymus.

We previously described a fibronectin/VLA-5-dependent impairment of NOD thymocyte migration, correlated with partial thymocyte arrest within thymic perivascular spaces. Yet, NOD thymocytes still emigrate, suggesting the involvement of other cell migration-related alterations. In this context, the aim of this work was to study the role of extracellular matrix ligands, alone or in combination wit...

Landsberg Curvature, S-curvature and Riemann Curvature

Symmetric curvature tensor

Recently, we have used the symmetric bracket of vector fields, and developed the notion of the symmetric derivation. Using this machinery, we have defined the concept of symmetric curvature. This concept is natural and is related to the notions divergence and Laplacian of vector fields. This concept is also related to the derivations on the algebra of symmetric forms which has been discu...

Curvature combs and curvature plots

We compare curvature combs and curvature plots. © 2016 Elsevier Ltd. All rights reserved.

CONNECTIONS, CURVATURE, AND p-CURVATURE

1.1. Connections and derivations. Let S be a scheme, and X smooth and finite type over S throughout. We have the rank-n vector bundle ΩX/S of 1-forms on X over S. We also fix some notation in the case that S is of characteristic p: in this case, we denote by FT the absolute Frobenius map for any scheme T , by X = X×S S the p-twist of X over S, where the map used in the fiber product is FS : S →...