Curvature of special almost Hermitian manifolds

Francisco Martín Cabrera and Andrew Swann

Vol. 228 (2006), No. 1, 165–184

DOI: 10.2140/pjm.2006.228.165

Abstract

We study the curvature of almost Hermitian manifolds and their special analogues via intrinsic torsion and representation theory. By deriving different formulae for the skew-symmetric part of the ∗-Ricci curvature, we find that some of these contributions are dependent on the approach used and, for the almost Hermitian case, we obtain tables that differ from those of Falcitelli, Farinola, and Salamon. We show how the exterior algebra may be used to explain some of these variations.

Keywords

almost Hermitian, special almost Hermitian, intrinsic torsion, curvature tensor, G-connection

Mathematical Subject Classification 2000

Primary: 53C55

Secondary: 53C10, 53C15

Milestones

Received: 10 January 2005

Accepted: 25 July 2005

Published: 1 November 2006