Deformed Hermitian Yang–Mills connections, extended gauge group and scalar curvature

Metrics of Positive Scalar Curvature and Connections with Surgery

Commutation Relationships and Curvature Spin-tensors for Extended Spinor Connections

Extended spinor connections associated with composite spin-tensorial bundles are considered. Commutation relationships for covariant and multivariate differentiations and corresponding curvature spin-tensors are derived.

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 →...

Hermitian Curvature Flow

We define a functional for Hermitian metrics using the curvature of the Chern connection. The Euler-Lagrange equation for this functional is an elliptic equation for Hermitian metrics. Solutions to this equation are related to Kähler-Einstein metrics, and are automatically Kähler-Einstein under certain conditions. Given this, a natural parabolic flow equation arises. We prove short time existen...

Constant Scalar Curvature Hypersurfaces in the Extended Schwarzschild Space-time

In this paper we study the spherically symmetric CSC hypersurfaces of the extended Schwarzschild space-time. Especially, we analyse the embedding equation and we find the family of solutions or slices that results varying a parameter c, for fixed CSC parameter a and fixed time-translation parameter t0. The parameter c represents the amount of variation of volume of the 3-geometry during the ‘ti...