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We determine the space of algebraic pseudo-Hermitian Kahler-Weyl curvature tensors and the space of para-Hermitian Kahler-Weyl curvature tensors in dimension 4 and show that every algebraic possibility is geometrically realizable. We establish the Gray identity for pseudo-Hermitian Weyl manifolds and for para-Hermitian Weyl manifolds in arbitrary dimension.
We show that a closed almost Kahler 4-manifold of globally constant holomorphic sectional curvature $kgeq 0$ with respect to the canonical Hermitian connection is automatically Kahler. The same result holds for $k<0$ if we require in addition that th
We study the local geometry of 4-manifolds equipped with a emph{para-Kahler-Einstein} (pKE) metric, a special type of split-signature pseudo-Riemannian metric, and their associated emph{twistor distribution}, a rank 2 distribution on the 5-dimensiona
We work in both the complex and in the para-complex categories and examine (para)-Kahler Weyl structures in both the geometric and in the algebraic settings. The higher dimensional setting is quite restrictive. We show that any (para)-Kaehler Weyl al
It is shown that on every closed oriented Riemannian 4-manifold $(M,g)$ with positive scalar curvature, $$int_M|W^+_g|^2dmu_{g}geq 2pi^2(2chi(M)+3tau(M))-frac{8pi^2}{|pi_1(M)|},$$ where $W^+_g$, $chi(M)$ and $tau(M)$ respectively denote the self-dual
A special Kahler-Ricci potential on a Kahler manifold is any nonconstant $C^infty$ function $tau$ such that $J( ablatau)$ is a Killing vector field and, at every point with $dtau e 0$, all nonzero tangent vectors orthogonal to $ ablatau$ and $J( abla