130 research outputs found
Some integrability conditions for almost K\"ahler manifolds
Among other results, a compact almost K\"ahler manifold is proved to be
K\"ahler if the Ricci tensor is semi-negative and its length coincides with
that of the star Ricci tensor or if the Ricci tensor is semi-positive and its
first order covariant derivatives are Hermitian. Moreover, it is shown that
there are no compact almost K\"ahler manifolds with harmonic Weyl tensor and
non-parallel semi-positive Ricci tensor. Stronger results are obtained in
dimension 4.Comment: Latex2e, 13 page
Lorentzian spacetimes with constant curvature invariants in three dimensions
In this paper we study Lorentzian spacetimes for which all polynomial scalar
invariants constructed from the Riemann tensor and its covariant derivatives
are constant (CSI spacetimes) in three dimensions. We determine all such CSI
metrics explicitly, and show that for every CSI with particular constant
invariants there is a locally homogeneous spacetime with precisely the same
constant invariants. We prove that a three-dimensional CSI spacetime is either
(i) locally homogeneous or (ii) it is locally a Kundt spacetime. Moreover, we
show that there exists a null frame in which the Riemann (Ricci) tensor and its
derivatives are of boost order zero with constant boost weight zero components
at each order. Lastly, these spacetimes can be explicitly constructed from
locally homogeneous spacetimes and vanishing scalar invariant spacetimes.Comment: 14 pages; Modified to match published versio
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