Some Results on 3-Dimensional Lorentzian Manifold
Abstract
In this paper, a necessary and sufficient condition for a function f(t; x; y)
of Walker 3-metric to have a vector field X, to be a Killing vector field, is constructed. Also, we determine Sezabo operator related to Ricci operator of Lorentzian 3-manifold. Finally, we construct a necessary and sufficient condition for a function f(t; x; y) of the Walker metric of 3-dimensional manifold, to have zero Sezabo operator.
of Walker 3-metric to have a vector field X, to be a Killing vector field, is constructed. Also, we determine Sezabo operator related to Ricci operator of Lorentzian 3-manifold. Finally, we construct a necessary and sufficient condition for a function f(t; x; y) of the Walker metric of 3-dimensional manifold, to have zero Sezabo operator.
Keywords
Killing vector, Lorentzian manifold, Sezabo operator, Walker manifold.
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