This item still needs to be validated !
Title: Three- and four-dimensional Einstein-like manifolds and homogeneity
Authors: Bueken, Peter ×
Vanhecke, Lieven #
Issue Date: 1999
Publisher: Kluwer academic publ
Series Title: Geometriae dedicata vol:75 issue:2 pages:123-136
Abstract: The aim of this paper is to study three- and four-dimensional Einstein-like Riemannian manifolds which are Ricci-curvature homogeneous, that is, have constant Ricci eigenvalues. In the three- dimensional case, we present the complete classification of these spaces while, in the four-dimensional case, this classification is obtained in the special case where the manifold is locally homogeneous. We also present explicit examples of four-dimensional locally homogeneous Riemannian manifolds whose Ricci tensor is cyclic-parallel (that is, are of type A) and has distinct eigenvalues. These examples are invalidating an expectation stated by F. Podesta and A. Spiro, and illustrating a striking contrast with the three- dimensional case (where this situation cannot occur). Finally, we also investigate the relation between three- and four-dimensional Einstein-like manifolds of type A and D'Atri spaces, that is, Riemannian manifolds whose geodesic symmetries are volume-preserving (up to sign).
ISSN: 0046-5755
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Geometry Section
Mathematics - miscellaneous
× corresponding author
# (joint) last author

Files in This Item:

There are no files associated with this item.

Request a copy


All items in Lirias are protected by copyright, with all rights reserved.

© Web of science