The geometry of modified Riemannian extensions-Reference-Cited by-同舟云学术

The geometry of modified Riemannian extensions

Published:2009-04-08 Issue:2107 Volume:465 Page:2023-2040
ISSN:1364-5021
Container-title:Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Proc. R. Soc. A.

Author:

Calviño-Louzao E.¹,García-Río E.¹,Gilkey P.²,Vázquez-Lorenzo R.¹

Affiliation:

1. Department of Geometry and Topology, Faculty of Mathematics, University of Santiago de Compostela15782 Santiago de Compostela, Spain

2. Department of Mathematics, University of OregonEugene, OR 97403, USA

Abstract

We show that every paracomplex space form is locally isometric to a modified Riemannian extension and gives necessary and sufficient conditions for a modified Riemannian extension to be Einstein. We exhibit Riemannian extension Osserman manifolds of signature (3, 3), whose Jacobi operators have non-trivial Jordan normal form and which are not nilpotent. We present new four-dimensional results in Osserman geometry.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2009.0046

Reference38 articles.

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