Two loop and all loop finite 4-metrics

In pure Einstein theory, Ricci flat Lorentzian 4-metrics of Petrov types III or N have vanishing counter terms up to and including two loops. Moreover for pp-waves and type-N spacetimes of Kundt's class which admit a non-twisting, non expanding, null congruence all possible invariants formed from the Weyl tensor and its covariant derivatives vanish. Thus these Lorentzian metrics suffer no quantum corrections to all loop orders. By contrast for complete non-singular Riemannian metrics the two loop counter term vanishes only if the metric is flat.Comment: 4 pages Latex file, no figure

Covariant derivative of the curvature tensor of pseudo-K\"ahlerian manifolds

It is well known that the curvature tensor of a pseudo-Riemannian manifold can be decomposed with respect to the pseudo-orthogonal group into the sum of the Weyl conformal curvature tensor, the traceless part of the Ricci tensor and of the scalar curvature. A similar decomposition with respect to the pseudo-unitary group exists on a pseudo-K\"ahlerian manifold; instead of the Weyl tensor one obtains the Bochner tensor. In the present paper, the known decomposition with respect to the pseudo-orthogonal group of the covariant derivative of the curvature tensor of a pseudo-Riemannian manifold is refined. A decomposition with respect to the pseudo-unitary group of the covariant derivative of the curvature tensor for pseudo-K\"ahlerian manifolds is obtained. This defines natural classes of spaces generalizing locally symmetric spaces and Einstein spaces. It is shown that the values of the covariant derivative of the curvature tensor for a non-locally symmetric pseudo-Riemannian manifold with an irreducible connected holonomy group different from the pseudo-orthogonal and pseudo-unitary groups belong to an irreducible module of the holonomy group.Comment: the final version accepted to Annals of Global Analysis and Geometr

Homogeneity and plane-wave limits

We explore the plane-wave limit of homogeneous spacetimes. For plane-wave limits along homogeneous geodesics the limit is known to be homogeneous and we exhibit the limiting metric in terms of Lie algebraic data. This simplifies many calculations and we illustrate this with several examples. We also investigate the behaviour of (reductive) homogeneous structures under the plane-wave limit.Comment: In memory of Stanley Hobert, 33 pages. Minor corrections and some simplification of Section 4.3.

Curvature homogeneous spacelike Jordan Osserman pseudo-Riemannian manifolds

Let s be at least 2. We construct Ricci flat pseudo-Riemannian manifolds of signature (2s,s) which are not locally homogeneous but whose curvature tensors never the less exhibit a number of important symmetry properties. They are curvature homogeneous; their curvature tensor is modeled on that of a local symmetric space. They are spacelike Jordan Osserman with a Jacobi operator which is nilpotent of order 3; they are not timelike Jordan Osserman. They are k-spacelike higher order Jordan Osserman for $2\le k\le s$; they are k-timelike higher order Jordan Osserman for $s+2\le k\le 2s$, and they are not k timelike higher order Jordan Osserman for $2\le s\le s+1$.Comment: Update bibliography, fix minor misprint

Methyl-β-Cyclodextrins Preferentially Remove Cholesterol from the Liquid Disordered Phase in Giant Unilamellar Vesicles

Methyl-β-cyclodextrins (MβCDs) are molecules that are extensively used to remove and to load cholesterol (Chol) from artificial and natural membranes; however, the mechanism of Chol extraction by MβCD from pure lipids or from complex mixtures is not fully understood. One of the outstanding questions in this field is the capability of MβCD to remove Chol from lipid domains having different packing. Here, we investigated the specificity of MβCD to remove Chol from coexisting macrodomains with different lipid packing. We used giant unilamellar vesicles (GUVs) made of 1,2-dioleoylphosphatidylcholine:1,2-dipalmitoylphatidylcholine:free cholesterol, 1:1:1 molar ratio at 27°C. Under these conditions, individual GUVs present Chol distributed into lo and ld phases. The two phases can be distinguished and visualized using Laurdan generalized polarization and two-photon excitation fluorescence microscopy. Our data indicate that MβCD removes Chol preferentially from the more disordered phase. The process of selective Chol removal is dependent on the MβCD concentration. At high concentrations, MβCD also removes phospholipids

Homogeneous quaternionic Kähler structures on eight-dimensional non-compact quaternion-Kähler symmetric spaces

For each non-compact quaternion-Kähler symmetric space of dimension 8, all of its descriptions as a homogeneous Riemannian space (obtained through the Witte’s refined Langlands decomposition) and the associated homogeneous quaternionic Kähler structures are studied