Nonnegatively curved Euclidean submanifolds in codimension two

We provide a classification of compact Euclidean submanifolds $M^n\subset{\mathbb{R}}^{n+2}$ with nonnegative sectional curvature, for $n\ge 3$. The classification is in terms of the induced metric (including the diffeomorphism classification of the manifold), and we study the structure of the immersions as well. In particular, we provide the first known example of a nonorientable quotient $({\mathbb{S}}^{n-1}\times{\mathbb{S}}^1)/{{\mathbb{Z}}_2}\subset{\mathbb{R}}^{n+2}$ with nonnegative curvature. For the 3-dimensional case, we show that either the universal cover is isometric to ${\mathbb{S}}^2\times{\mathbb{R}}$, or $M^3$ is diffeomorphic to a lens space, and the complement of the (nonempty) set of flat points is isometric to a twisted cylinder $(N^2\times{\mathbb{R}})/{\mathbb{Z}}$. As a consequence we conclude that, if the set of flat points is not too big, there exists a unique flat totally geodesic surface in $M^3$ whose complement is the union of one or two twisted cylinders over disks.Comment: Accepted for publication in Commentarii Mathematici Helvetic

Topological obstructions to fatness

Alan Weinstein showed that certain characteristic numbers of any Riemannian submersion with totally geodesic fibers and positive vertizontal curvatures are nonzero. In this paper we explicitly compute these invariants in terms of Chern and Pontrjagin numbers of the bundle. This allows us to show that many bundles do not admit such metrics.Comment: 32 pages. To appear in Geom. Topo

New string vacua from twistor spaces

We find a new family of AdS_4 vacua in IIA string theory. The internal space is topologically either the complex projective space CP^3 or the "flag manifold" SU(3)/(U(1)xU(1)), but the metric is in general neither Einstein nor Kaehler. All known moduli are stabilized by fluxes, without using quantum effects or orientifold planes. The analysis is completely ten--dimensional and does not rely on assumptions about Kaluza--Klein reduction.Comment: 19 pages. v3: published version, further minor correction

Superconductivity without Fe or Ni in the phosphides BaIr2P2 and BaRh2P2

Heat capacity, resistivity, and magnetic susceptibility measurements confirm bulk superconductivity in single crystals of BaIr$_2$P$_2$ (T$_c$=2.1K) and BaRh$_2$P$_2$ (T$_c$ = 1.0 K). These compounds form in the ThCr$_2$Si$_2$ (122) structure so they are isostructural to both the Ni and Fe pnictides but not isoelectronic to either of them. This illustrates the importance of structure for the occurrence of superconductivity in the 122 pnictides. Additionally, a comparison between these and other ternary phosphide superconductors suggests that the lack of interlayer $P-P$ bonding favors superconductivity. These stoichiometric and ambient pressure superconductors offer an ideal playground to investigate the role of structure for the mechanism of superconductivity in the absence of magnetism.Comment: Published in Phys Rev B: Rapid Communication

Crystal Structure of 2-(2,6-diisopropylphenyl)-N,Ndiethyl- 3,3-dimethyl-2-azaspiro[4.5]decan-1- amine: A Diethylamine Adduct of a Cyclic(alkyl)- (amino)carbene (CAAC)

The structure of the title compound, C27H46N2, at 93 K has monoclinic (P21/n) symmetry. The title compound was prepared by treatment of 2-(2,6-diiso­propyl­phenyl)-3,3-dimethyl-2-aza­spiro­[4.5]dec-1-en-2-ium hydrogen dichloride with two equivalents of lithium di­ethyl­amide. Characterization of the title compound by single-crystal X-ray diffraction and 1H and 13C NMR spectroscopy is presented. Formation of the di­ethyl­amine adduct of the cyclic(alk­yl)(amino)­carbene (CAAC) was unexpected, as deprotonation using lithium diiso­propyl­amide results in free CAAC formation

Crystal Structure of 2-(2,6-diiso­propyl­phen­yl)-N,N-diethyl-3,3-dimethyl-2-aza­spiro­[4.5]decan-1-amine: A Di­ethyl­amine Adduct of a Cyclic(alk­yl)(amino)­carbene (CAAC)

The structure of the title compound, C27H46N2, at 93 K has monoclinic (P21/n) symmetry. The title compound was prepared by treatment of 2-(2,6-diiso­propyl­phenyl)-3,3-dimethyl-2-aza­spiro­[4.5]dec-1-en-2-ium hydrogen dichloride with two equivalents of lithium di­ethyl­amide. Characterization of the title compound by single-crystal X-ray diffraction and 1H and 13C NMR spectroscopy is presented. Formation of the di­ethyl­amine adduct of the cyclic(alk­yl)(amino)­carbene (CAAC) was unexpected, as deprotonation using lithium diiso­propyl­amide results in free CAAC formation

Reduzierung des Zuckerkonsums für eine bessere Mundgesundheit – Welche Strategien sind Erfolg versprechend? [Reducing sugar consumption to improve oral health-which strategies are effective?]

Health promotion strategies can make a significant contribution to the prevention of non-communicable diseases. The most important non-communicable diseases affecting the mouth and teeth are dental caries and periodontal disease. Sugar is a causal factor in the development of dental caries, obesity and obesity-related diseases. Sugar is therefore recognised as an important commercial determinant of health and a public health priority. However, existing strategies to reduce sugar consumption often focus on individual behaviour change while ignoring the role of the wider social and commercial environment.In this article we describe the current recommendations on sugar intake made by the World Health Organization, existing data on sugar intake in Germany as well as the social and commercial factors that influence sugar consumption. Important public health principles will be outlined, followed by a discussion of appropriate sugar reduction strategies. Examples for upstream and downstream approaches to prevention are presented and opportunities for dental health professionals to influence policy and practice highlighted