39 research outputs found
Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups
Together with spaces of constant sectional curvature and products of a real
line with a manifold of constant curvature, the socalled Egorov spaces and
-spaces exhaust the class of -dimensional Lorentzian manifolds
admitting a group of isometries of dimension at least , for
almost all values of [Patrangenaru V., Geom. Dedicata 102 (2003), 25-33].
We shall prove that the curvature tensor of these spaces satisfy several
interesting algebraic properties. In particular, we will show that Egorov
spaces are Ivanov-Petrova manifolds, curvature-Ricci commuting (indeed,
semi-symmetric) and -spaces, and that -spaces are
Ivanov-Petrova and curvature-curvature commuting manifolds
Ricci Solitons on Lorentzian Manifolds with Large Isometry Groups
We show that Lorentzian manifolds whose isometry group is of dimension at
least are expanding, steady and shrinking Ricci solitons
and steady gradient Ricci solitons. This provides examples of complete locally
conformally flat and symmetric Lorentzian Ricci solitons which are not rigid
Some general new Einstein Walker manifolds
In this paper, Lie symmetry group method is applied to find the lie point
symmetries group of a PDE system that is determined general form of
four-dimensional Einstein Walker manifold. Also we will construct the optimal
system of one-dimensional Lie subalgebras and investigate some of its group
invariant solutions.Comment: 14 page
Stanilov-Tsankov-Videv Theory
We survey some recent results concerning Stanilov-Tsankov-Videv theory,
conformal Osserman geometry, and Walker geometry which relate algebraic
properties of the curvature operator to the underlying geometry of the
manifold.Comment: This is a contribution to the Proceedings of the 2007 Midwest
Geometry Conference in honor of Thomas P. Branson, published in SIGMA
(Symmetry, Integrability and Geometry: Methods and Applications) at
http://www.emis.de/journals/SIGMA