Article
Licensed
Unlicensed
Requires Authentication
Relating the curvature tensor and the complex Jacobi operator of an almost Hermitian manifold
-
M. Brozos-Vázquez
Published/Copyright:
September 11, 2008
Abstract
Let J be a unitary almost complex structure on a Riemannian manifold (M, g). If x is a unit tangent vector, let π := Span{x, Jx} be the associated complex line in the tangent bundle of M. The complex Jacobi operator and the complex curvature operators are defined, respectively, by 
and 
. We show that if (M, g) is Hermitian or if (M, g) is nearly Kähler, then either the complex Jacobi operator or the complex curvature operator completely determine the full curvature operator; this generalizes a well known result in the real setting to the complex setting. We also show that this result fails for general almost Hermitian manifolds.
Key words.: Complex curvature operator; complex Jacobi operator; almost Hermitian manifold; Hermitian manifold; nearly Kähler manifold
Received: 2006-11-15
Published Online: 2008-09-11
Published in Print: 2008-August
© de Gruyter 2008
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- A rigidity result for domains with a locally strictly convex point
- On the geometry of Grassmannian equivalent connections
- On Lie groups as quasi-Kähler manifolds with Killing Norden metric
- Relating the curvature tensor and the complex Jacobi operator of an almost Hermitian manifold
- A characterization of m-ovoids and i-tight sets of polar spaces
- On Grassmann secant extremal varieties
- Almost del Pezzo manifolds
- Projective models of K3 surfaces with an even set
- Nonrational del Pezzo fibrations
- Principal bundles over a smooth real projective curve of genus zero
Keywords for this article
Complex curvature operator;
complex Jacobi operator;
almost Hermitian manifold;
Hermitian manifold;
nearly Kähler manifold
Articles in the same Issue
- A rigidity result for domains with a locally strictly convex point
- On the geometry of Grassmannian equivalent connections
- On Lie groups as quasi-Kähler manifolds with Killing Norden metric
- Relating the curvature tensor and the complex Jacobi operator of an almost Hermitian manifold
- A characterization of m-ovoids and i-tight sets of polar spaces
- On Grassmann secant extremal varieties
- Almost del Pezzo manifolds
- Projective models of K3 surfaces with an even set
- Nonrational del Pezzo fibrations
- Principal bundles over a smooth real projective curve of genus zero
