Special almost Hermitian geometry

We study the classification of special almost hermitian manifolds in Gray and Hervella's type classes. We prove that the exterior derivatives of the symplectic form and the complex volume form contain all the information about the intrinsic torsion of the \SUn(n)-structure. Furthermore, we apply the obtained results to almost hyperhermitian geometry. Thus, we show that the exterior derivatives of the three K{\"a}hler forms of an almost hyperhermitian manifold are sufficient to determine the three covariant derivatives of such forms, i.e., the three mentioned exterior derivatives determine the intrinsic torsion of the {\sl Sp}(n)-structure.Comment: 27 page

SU(3)-structures on submanifolds of a Spin(7)-manifold

Local SU(3)-structures on an oriented submanifold of Spin(7)-manifold are determined and their types are characterized in terms of the shape operator and the type of the Spin(7)-structure. An application to Bryant \cite{MR89b:53084} and Calabi \cite{MR24 #A558} examples is given. It is shown that the product of a Cayley plane and a minimal surface lying in a four-dimensional orthogonal Cayley plane with the induced complex structure from the octonions described by Bryant in \cite{MR89b:53084} admits a holomorphic local complex volume form exactly when it lies in a three-plane, i.e. it coincides with the example constructed by Calabi in \cite{MR24 #A558}. In this case the holomorphic (3,0)-form is parallel with respect to the unique Hermitian connection with totally skew-symmetric torsion.Comment: 25 pages, no figures, some improvements and clarifications are made, final version to appear in Diff. Geom. App

High-Mass, Four-Planet Models for HR 8799: Constraining the Orbital Inclination and Age of the System

Debates regarding the age and inclination of the planetary system orbiting HR 8799, and the release of additional astrometric data following the discovery of the fourth planet prompted us to examine the possibility of constraining these two quantities by studying the long-term stability of this system at different orbital inclinations and in its high-mass configuration (7-10-10-10 MJup). We carried out ~1.5 million N-body integrations for different combinations of orbital elements of the four planets. The most dynamically stable combinations survived less than ~5 Myr at inclinations of 0{\deg} and 13{\deg}, and 41, 46, and 31 Myr at 18{\deg}, 23{\deg}, and 30{\deg}, respectively. Given such short lifetimes and the location of the system on the age-luminosity diagram for low-mass objects, the most reasonable conclusion of our study is that the planetary masses are less than 7-10-10-10 MJup and the system is quite young. Two trends to note from our work are as follows. (1) In the most stable systems, the higher the inclination, the more the coordinates for planets b and c diverge from the oldest archival astrometric data (released after we completed our N-body integrations), suggesting that either these planets are in eccentric orbits or have lower orbital inclinations than that of planet d. (2) The most stable systems place planet e closer to the central star than is observed, supporting the conclusion that the planets are more massive and the system is young. We present the details of our simulations and discuss the implications of the results.Comment: Content: 25 pages, 5 figures, 1 table. Submitted for publication on 2012 January 2. Accepted for publication in the Astrophysical Journal on June 7, 2012. File updated June 9, 201

Curvature decomposition of G_2 manifolds

Explicit formulas for the $G_2$-components of the Riemannian curvature tensor on a manifold with a $G_2$ structure are given in terms of Ricci contractions. We define a conformally invariant Ricci-type tensor that determines the 27-dimensional part of the Weyl tensor and show that its vanishing on compact $G_2$ manifold with closed fundamental form forces the three-form to be parallel. A topological obstruction for the existence of a $G_2$ structure with closed fundamental form is obtained in terms of the integral norms of the curvature components. We produce integral inequalities for closed $G_2$ manifold and investigate limiting cases. We make a study of warped products and cohomogeneity-one $G_2$ manifolds. As a consequence every Fern\'andez-Gray type of $G_2$ structure whose scalar curvature vanishes may be realized such that the metric has holonomy contained in $G_2$.Comment: LaTeX 2e, 26 pages, 2 tables. Changes in version 2: shortened, reorganized, misprints corrected, several remarks and new introduction. A formula in the proof of Theorem 1.2a has been corrected. Submitte

Lithium in LP 944-20

The definitive version is available at www.blackwell-synergy.com. Copyright Blackwell Publishing DOI :10.1111/j.1365-2966.2007.12182.xPeer reviewe

Disclosing intrinsic molecular dynamics on the 1-fs scale through extreme-ultraviolet pump-probe measurements

Through frequency up-conversion of polarization-shaped, femtosecond laser pulses nonlinearly interacting with xenon atoms, energetic, broadband, coherent, XUV continuum radiation is generated. By exploiting the thus-formed short-duration XUV pulses, all the optically allowed excited states of H2 are coherently populated. Nuclear and electronic 1-fs-scale dynamics are subsequently investigated by means of XUV-pump-XUV-probe measurements, which are compared to the results of ab initio calculations. The revealed dynamics reflects the intrinsic molecular behavior, as the XUV probe pulse hardly distorts the molecular potentialThis work is supported in part by the European Commission programs ATTOFEL, CRISP, Laserlab Europe, the European COST Actions MPI1203-SKO and CM1204 XLIC, and the Greek funding program NSRF. A.P. and F.M. acknowledge allocation of computer time by CCC-UAM and BSC Mare Nostrum, and financial support from the Advanced Grant of the European Research Council XCHEM (No. 290853), the European grant MC-RG ATTOTREND, the MICINN Project (No. FIS2010-15127), and the ERA-Chemistry Project (No. PIM2010EEC-00751)

Rotational Broadening and Doppler Tomography of the Quiescent X-Ray Nova Centaurus X-4

We present high and intermediate resolution spectroscopy of the X-ray nova Centaurus X-4 during its quiescent phase. Our analysis of the absorption features supports a K3-K5V spectral classification for the companion star, which contributes approximately 75 % of the total flux at Halpha. Using the high resolution spectra we have measured the secondary star's rotational broadening to be V_rot*sin(i) = 43 +/- 6 km/s and determined a binary mass ratio of q=0.17 +/- 0.06. Combining our results for K_2 and q with the published limits for the binary inclination, we constrain the mass of the compact object and the secondary star to the ranges 0.49 < M_1 < 2.49 Msun and 0.04 < M_2 < 0.58 Msun. A Doppler image of the Halpha line shows emission coming from the secondary star, but no hotspot is present. We discuss the possible origins of this emission.Comment: 10 pages, 4 figures, accepted by MNRA