Classification des variétés approximativement kähleriennes homogènes

International audienceWe prove Gray & Wolf's conjecture that a Riemannian homogeneous manifold admitting a strict nearly Kahler structure is 3-symmetric. We actually classify them in dimension 6 and use previous results of Swann, Cleyton and Nagy to prove the conjecture in higher dimensions

Twistors and 3-symmetric spaces

We describe complex twistor spaces over inner 3-symmetric spaces $G/H$, such that $H$ acts transitively on the fibre. Like in the symmetric case, these are flag manifolds $G/K$ where $K$ is the centralizer of a torus in $G$. Moreover, they carry an almost complex structure defined using the horizontal distribution of the normal connection on $G/H$, that coincides with the complex structure associated to a parabolic subgroup $P \subset G^{\mathbb C}$ if it is integrable. Conversely, starting from a complex flag manifold $G^{\mathbb C}/P$, there exists a natural fibration with complex fibres on a 3-symmetric space, called fibration of degree 3

A Nearly Quaternionic Structure on SU(3)

It is shown that the compact Lie group SU(3) admits an Sp(2)Sp(1)-structure whose distinguished 2-forms $\omega_1,\omega_2,\omega_3$ span a differential ideal. This is achieved by first reducing the structure further to a subgroup isomorphic to SO(3)

Strictly nearly Kahler 6-manifolds are not compatible with symplectic forms

We show that the almost complex structure underlying a non-Kahler, nearly Kahler 6-manifold (in particular, the standard almost complex structure of S^6) cannot be compatible with any symplectic form, even locally.Comment: 6 pages. to appear in CRAS. typos and quotations correcte

Mid- to late Holocene seasonal variability in northern Germany and adjacent oceans and its potential impact on human societies

In northern Germany and southern Scandinavia, the onset of farming around 6000 cal. yrs BP occurred coincidentally with one of the cold events recorded from the North Atlantic. It is therefore discussed whether the transition towards a Neolithic subsistence in this region could have been shaped by climate change. However, at a regional scale, high resolution climate reconstructions are lacking or missing the sensitivity to record abrupt climate changes. Indeed, most of these reconstructions represent the mean annual or summer climate variability, while some evidence show that winter variability in the North Hemisphere plays an important role during major rapid climate changes of the Holocene. The strength of this thesis lies in the reconstruction of winter climate variability during the mid- and late Holocene. Here, winter and warm season thermal reconstructions are based on benthic foraminifera Mg/Ca and oxygen isotopes from two Skagerrak cores. Cold events, roughly corresponding to the Atlantic Bond events, are evidenced during winter in the Skagerrak region over the mid- and late Holocene, and only partially during the warm season. Interestingly, an abrupt cooling between 6200 and 5900 cal. yrs BP, only found during winter, coincides with the onset of neolithisation in northern Germany and southern Scandinavia. Most likely, it resulted in a shortening of the vegetation growing season and an increased Baltic sea-ice extent that probably affected the marine food resources. In turn, these environmental changes must have lead the hunter-gatherer-fisher communities to abandon their previous subsistence strategies and adopt an economy based on agriculture. Other changes in subsistence and material culture from societies in the region coincide with climate changes recorded in the Skagerrak during the mid- to late Holocene transition, and are discussed in this thesis. The origin of short term variability found in the climate records is also discussed

6-dimensional nearly Kaehler manifolds of cohomogeneity one

We consider 6-dimensional strict nearly Kaehler manifolds acted on by a compact, cohomogeneity one automorphism group G. We classify the compact manifolds of this class up to G-diffeomorphisms. We also prove that the manifold has constant sectional curvature whenever the group G is simple.Comment: 14 page