The Dirac operator on generalized Taub-NUT spaces

We find sufficient conditions for the absence of harmonic $L^2$ spinors on spin manifolds constructed as cone bundles over a compact K\"ahler base. These conditions are fulfilled for certain perturbations of the Euclidean metric, and also for the generalized Taub-NUT metrics of Iwai-Katayama, thus proving a conjecture of Vi\csinescu and the second author.Comment: Final version, 16 page

Transformations of locally conformally K\"ahler manifolds

We consider several transformation groups of a locally conformally K\"ahler manifold and discuss their inter-relations. Among other results, we prove that all conformal vector fields on a compact Vaisman manifold which is neither locally conformally hyperk\"ahler nor a diagonal Hopf manifold are Killing, holomorphic and that all affine vector fields with respect to the minimal Weyl connection of a locally conformally K\"ahler manifold which is neither Weyl-reducible nor locally conformally hyperk\"ahler are holomorphic and conformalComment: 8 page

Pseudo-Riemannian manifolds with recurrent spinor fields

The existence of a recurrent spinor field on a pseudo-Riemannian spin manifold $(M,g)$ is closely related to the existence of a parallel 1-dimensional complex subbundle of the spinor bundle of $(M,g)$. We characterize the following simply connected pseudo-Riemannian manifolds admitting such subbundles in terms of their holonomy algebras: Riemannian manifolds; Lorentzian manifolds; pseudo-Riemannian manifolds with irreducible holonomy algebras; pseudo-Riemannian manifolds of neutral signature admitting two complementary parallel isotropic distributions.Comment: 13 pages, the final versio

Spectral Bounds for Dirac Operators on Open Manifolds

We extend several classical eigenvalue estimates for Dirac operators on compact manifolds to noncompact, even incomplete manifolds. This includes Friedrich's estimate for manifolds with positive scalar curvature as well as the author's estimate on surfaces.Comment: pdflatex, 14 pages, 3 figure

Triangulated Surfaces in Twistor Space: A Kinematical Set up for Open/Closed String Duality

We exploit the properties of the three-dimensional hyperbolic space to discuss a simplicial setting for open/closed string duality based on (random) Regge triangulations decorated with null twistorial fields. We explicitly show that the twistorial N-points function, describing Dirichlet correlations over the moduli space of open N-bordered genus g surfaces, is naturally mapped into the Witten-Kontsevich intersection theory over the moduli space of N-pointed closed Riemann surfaces of the same genus. We also discuss various aspects of the geometrical setting which connects this model to PSL(2,C) Chern-Simons theory.Comment: 35 pages, references added, slightly revised introductio

A splitting theorem for Kahler manifolds whose Ricci tensors have constant eigenvalues

It is proved that a compact Kahler manifold whose Ricci tensor has two distinct, constant, non-negative eigenvalues is locally the product of two Kahler-Einstein manifolds. A stronger result is established for the case of Kahler surfaces. Irreducible Kahler manifolds with two distinct, constant eigenvalues of the Ricci tensor are shown to exist in various situations: there are homogeneous examples of any complex dimension n > 1, if one eigenvalue is negative and the other positive or zero, and of any complex dimension n > 2, if the both eigenvalues are negative; there are non-homogeneous examples of complex dimension 2, if one of the eigenvalues is zero. The problem of existence of Kahler metrics whose Ricci tensor has two distinct, constant eigenvalues is related to the celebrated (still open) Goldberg conjecture. Consequently, the irreducible homogeneous examples with negative eigenvalues give rise to complete, Einstein, strictly almost Kahler metrics of any even real dimension greater than 4.Comment: 18 pages; final version; accepted for publication in International Journal of Mathematic

Parallel spinors and holonomy groups

In this paper we complete the classification of spin manifolds admitting parallel spinors, in terms of the Riemannian holonomy groups. More precisely, we show that on a given n-dimensional Riemannian manifold, spin structures with parallel spinors are in one to one correspondence with lifts to Spin_n of the Riemannian holonomy group, with fixed points on the spin representation space. In particular, we obtain the first examples of compact manifolds with two different spin structures carrying parallel spinors.Comment: 10 pages, LaTeX2

Collisions of particles in locally AdS spacetimes II Moduli of globally hyperbolic spaces

We investigate 3-dimensional globally hyperbolic AdS manifolds containing "particles", i.e., cone singularities of angles less than $2\pi$ along a time-like graph $\Gamma$. To each such space we associate a graph and a finite family of pairs of hyperbolic surfaces with cone singularities. We show that this data is sufficient to recover the space locally (i.e., in the neighborhood of a fixed metric). This is a partial extension of a result of Mess for non-singular globally hyperbolic AdS manifolds.Comment: 29 pages, 3 figures. v2: 41 pages, improved exposition. To appear, Comm. Math. Phys. arXiv admin note: text overlap with arXiv:0905.182

Increased angiogenic factor secretion by decidual natural killer cells from pregnancies with high uterine artery resistance alters trophoblast function.

STUDY QUESTION Are the concentrations of factors secreted by decidual natural killer (dNK) cells from pregnancies at high risk of poor spiral artery remodelling different to those secreted from pregnancies at low risk? SUMMARY ANSWER Expression levels of PLGF, sIL-2R, endostatin and angiogenin were significantly increased by dNK cells from high-risk pregnancies, and angiogenin and endostatin were found to alter trophoblast function. WHAT IS KNOWN ALREADY During early pregnancy, maternal uterine spiral arteries are remodelled from small diameter, low-flow, high-resistance vessels into larger diameter, higher flow vessels, with low-resistance. This change is essential for the developing fetus to obtain sufficient oxygen and nutrients. dNK cells have been implicated in this process. STUDY DESIGN, SIZE, DURATION dNK cells were isolated from first trimester terminations of pregnancies (obtained with local ethical approval) screened for normal- or high-resistance index, indicative of cases least (21%) likely to have developed pre-eclampsia had the pregnancy not been terminated (n = 18 each group). Secreted factors and the effects of these on the trophoblast cell line, SGHPL-4, were assessed in vitro. PARTICIPANTS/MATERIALS, SETTING, METHODS A multiplex assay was used to assess dNK cell-secreted factors. SGHPL-4 cell functions were assessed using time-lapse microscopy, 3D invasion assays, endothelial-like tube formation ability and western blot analysis. MAIN RESULTS AND THE ROLE OF CHANCE The expression levels of PLGF (P < 0.01), sIL-2R (P < 0.01), endostatin (P < 0.05) and angiogenin (P < 0.05) were significantly increased by dNK cells from high-risk pregnancies. Endostatin significantly decreased SGHPL-4 invasion (P < 0.05), SGHPL-4 tube formation (P < 0.05) and SGHPL-4 Aktser473 phosphorylation (P < 0.05). Angiogenin significantly decreased SGHPL-4 invasion (P < 0.05), but increased SGHPL-4 tube formation (P < 0.01) and decreased SGHPL-4 Aktser473 phosphorylation (P < 0.05). LIMITATIONS, REASONS FOR CAUTION The culture of dNK cells and protein concentrations in vitro may not fully represent the in vivo situation. Although SGHPL-4 cells are extravillous trophoblast derived, further studies would be needed to confirm the roles of angiogenin and endostatin in vivo. WIDER IMPLICATIONS OF THE FINDINGS The altered expression of secreted factors of dNK cells may contribute to pregnancy disorders associated with poor spiral artery remodelling. STUDY FUNDING/COMPETING INTEREST(S) This study was supported by the Wellcome Trust (project reference 091550). R.F. was a recipient of a PhD studentship from the Division of Biomedical Sciences, St. George's, University of London. The authors have no conflict of interests

On the supersymmetries of anti de Sitter vacua

We present details of a geometric method to associate a Lie superalgebra with a large class of bosonic supergravity vacua of the type AdS x X, corresponding to elementary branes in M-theory and type II string theory.Comment: 16 page