Stability of higher order singular points of Poisson manifolds and Lie algebroids

We study the stability of singular points for smooth Poisson structures as well as general Lie algebroids. We give sufficient conditions for stability lying on the first (not necessarily linear) approximation of the given Poisson structure or Lie algebroid at a singular point. The main tools used here are the classical Lichnerowicz-Poisson cohomology and the deformation cohomology for Lie algebroids recently introduced by Crainic and Moerdijk. We also provide several examples of stable singular points of order $k \geq 1$ for Poisson structures and Lie algebroids. Finally, we apply our results to pre-symplectic leaves of Dirac manifolds.Comment: corrected typo

On the local structure of Dirac manifolds

We give a local normal form for Dirac structures. As a consequence, we show that the dimensions of the pre-symplectic leaves of a Dirac manifold have the same parity. We also show that, given a point $m$ of a Dirac manifold $M$, there is a well-defined transverse Poisson structure to the pre-symplectic leaf $P$ through $m$. Finally, we describe the neighborhood of a pre-symplectic leaf in terms of geometric data. This description agrees with that given by Vorobjev for the Poisson caseComment: minor correction

Generalized Contact Structures

We study integrability of generalized almost contact structures, and find conditions under which the main associated maximal isotropic vector bundles form Lie bialgebroids. These conditions differentiate the concept of generalized contact structures from a counterpart of generalized complex structures on odd-dimensional manifolds. We name the latter strong generalized contact structures. Using a Boothby-Wang construction bridging symplectic structures and contact structures, we find examples to demonstrate that, within the category of generalized contact structures, classical contact structures have non-trivial deformations. Using deformation theory of Lie bialgebroids, we construct new families of strong generalized contact structures on the three-dimensional Heisenberg group and its co-compact quotients.Comment: 35 pages. To appear in Journal of LM

VB-Courant algebroids, E-Courant algebroids and generalized geometry

In this paper, we first discuss the relation between VB-Courant algebroids and E-Courant algebroids and construct some examples of E-Courant algebroids. Then we introduce the notion of a generalized complex structure on an E-Courant algebroid, unifying the usual generalized complex structures on even-dimensional manifolds and generalized contact structures on odd-dimensional manifolds. Moreover, we study generalized complex structures on an omni-Lie algebroid in detail. In particular, we show that generalized complex structures on an omni-Lie algebra \gl(V)\oplus V correspond to complex Lie algebra structures on V.Comment: 19 page

Deformations of pairs of codimension one foliations

The notion of a linear deformation of a codimension one foliation into contact structures was introduced in [5]. This concept is a special type of deformation of confoliations. In this paper, we study linear deformations of pairs of codimension one foliations into contact pairs. Applications of our main result are also given

Conformal Dirac Structures

The Courant bracket defined originally on the sections of the vector bundle TM ⊕ T*M → M is extended to the direct sum of the 1-jet vector bundle and its dual. The extended bracket allows one to interpret many structures encountered in differential geometry in terms of Dirac structures. We give here a new approach to conformal Jacobi structures

Generalized Kählerian manifolds and transformation of generalized contact structures

summary:The aim of this paper is two-fold. First, new generalized Kähler manifolds are constructed starting from both classical almost contact metric and almost Kählerian manifolds. Second, the transformation construction on classical Riemannian manifolds is extended to the generalized geometry setting

A systematic study on volumetric and transport properties of binary systems 1-propanol + n-hexadecane, 1-butanol + n-hexadecane and 1-propanol + ethyl oleate at different temperatures: Experimental and modeling

Densities (rho), viscosities (eta), speed of sounds (u) and refractive indices (n(D)) at temperature range (293.15-343.15) K with 5 K interval, for three binary mixtures (1-propanol + n-hexadecane, 1-butanol + n-hexadecane and 1-propanol + ethyl oleate), were measured at atmospheric pressure. Based on the corresponding experimental data, excess molar volume (V-E), viscosity deviation (Delta eta) and deviation in refractive index (Delta n(D)) have been calculated. Beside these properties, molar excess Gibbs free energies of activation of viscous flow (Delta*G(E)) and deviation in isentropic compressibility (Delta k(s)) were calculated from measured density, viscosity and speed of sound data. The excess/deviation functions have been fitted by Redlich-Kister equation and discussed in terms of molecular interactions existing in the mixtures. Viscosity modeling was performed using four models: UNIFAC-VISCO, ASOG-VISCO, Teja-Rice and McAllister. Experimental viscosity data have been used to determine new binary UNIFAC-VISCO and ASOG-VISCO interaction parameters and the interaction parameters for correlation models by applying some optimization technique. For all systems, positive deviations were observed for the excess molar volumes in the whole concentration range. A negative deviation and an inversion sign for the excess dynamic viscosity were observed in the systems of 1-butanol + n-hexadecane and 1-propanol + n-hexadecane, respectively, while positive deviation was observed for 1-propanol + ethyl oleate mixture. The results of viscosity modeling showed that four-body McAllister models are suitable to describe viscosities for all systems and temperatures with maximum percentage deviations (PDmax) less than 0.5%