Almost Osserman structures on natural Riemann extensions
type: Item
instance of: scholarly article
title: Almost Osserman structures on natural Riemann extensions
zbMATH Open document ID: 1277.53016
author: Masami Sekizawa
author: Oldřich Kowalski
published in: Differential Geometry and its Applications
publication date: 2013-03-05T00:00:00Z
review text: In the present paper, the authors study natural Einstein-Riemann extensions of torsion-free affine manifolds. The Riemann extension of such a manifold of dimension \(n\) is a pseudo-Riemannian manifold of signature \((n,n)\). It is proven that the natural Einstein-Riemann extension of a direct product of any number of non-flat torsion-free affine two-dimensional manifolds with skew-symmetric Ricci tensors and of a flat affine space is an almost Osserman manifold in the sense that the Jacobi operator has to be restricted from the whole set of space-like unit vectors (or time-like unit vectors, respectively) to a complement of a subset of measure zero. It is also shown that the characteristic polynomial of the (restricted) Jacobi operator in the cotangent bundle depends only on the full dimension \(n\) of the base manifold and remains the same as for the flat affine space.
reviewed by: Raina Ivanova
Mathematics Subject Classification ID: 53B05
Mathematics Subject Classification ID: 53B30
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 6141628
zbMATH Keywords: affine connections
zbMATH Keywords: Jacobi operator
zbMATH Keywords: Einstein space
zbMATH Keywords: natural Riemann extension
zbMATH Keywords: Osserman manifold
MaRDI profile type: Publication
full work available at URL: j.difgeo.2012.10.007
OpenAlex ID: W2007675546
Wikidata QID: Q115356657
DOI: 10.1016/J.DIFGEO.2012.10.007
Recommended article: On natural Riemann extensions
Recommended article: Affine Osserman connections and their Riemann extensions
Recommended article: On some differential operators on natural Riemann extensions
Recommended article: Extensions of Riemann surfaces in topological algebras
Recommended article: On rational structures and their asymptotics
Recommended article: Theorems for extension on manifolds with almost complex structures
Recommended article: Q3778985
Recommended article: Projective structures on Riemann surface and natural differential operators
Recommended article: Relative Riemann-Zariski spaces
Recommended article: Q4812119
description: scientific article; zbMATH DE number 6141628