3-quasi-Sasakian manifolds

In the present paper we carry on a systematic study of 3-quasi-Sasakian manifolds. In particular we prove that the three Reeb vector fields generate an involutive distribution determining a canonical totally geodesic and Riemannian foliation. Locally, the leaves of this foliation turn out to be Lie groups: either the orthogonal group or an abelian one. We show that 3-quasi-Sasakian manifolds have a well-defined rank, obtaining a rank-based classification. Furthermore, we prove a splitting theorem for these manifolds assuming the integrability of one of the almost product structures. Finally, we show that the vertical distribution is a minimum of the corrected energy.Comment: 17 pages, minor modifications, references update

On certain surfaces in the Euclidean space E3{\mathbb{E}}^3

In the present paper we classify all surfaces in \E^3 with a canonical principal direction. Examples of these type of surfaces are constructed. We prove that the only minimal surface with a canonical principal direction in the Euclidean space ${\mathbb{E}}^3$ is the catenoid.Comment: 13 Latex page

Toric moment mappings and Riemannian structures

Coadjoint orbits for the group SO(6) parametrize Riemannian G-reductions in six dimensions, and we use this correspondence to interpret symplectic fibrations between these orbits, and to analyse moment polytopes associated to the standard Hamiltonian torus action on the coadjoint orbits. The theory is then applied to describe so-called intrinsic torsion varieties of Riemannian structures on the Iwasawa manifold.Comment: 25 pages, 14 figures; Geometriae Dedicata 2012, Toric moment mappings and Riemannian structures, available at http://www.springerlink.com/content/yn86k22mv18p8ku2

Canonical-type connection on almost contact manifolds with B-metric

The canonical-type connection on the almost contact manifolds with B-metric is constructed. It is proved that its torsion is invariant with respect to a subgroup of the general conformal transformations of the almost contact B-metric structure. The basic classes of the considered manifolds are characterized in terms of the torsion of the canonical-type connection.Comment: 11 pages, The final publication is available at http://www.springerlink.co

On the characteristic connection of gwistor space

We give a brief presentation of gwistor space, which is a new concept from G_2 geometry. Then we compute the characteristic torsion T^c of the gwistor space of an oriented Riemannian 4-manifold with constant sectional curvature k and deduce the condition under which T^c is \nabla^c-parallel; this allows for the classification of the G_2 structure with torsion and the characteristic holonomy according to known references. The case with the Einstein base manifold is envisaged.Comment: Many changes since first version, including title; Central European Journal of Mathematics, 201

Lines, Circles, Planes and Spheres

Let $S$ be a set of $n$ points in $\mathbb{R}^3$, no three collinear and not all coplanar. If at most $n-k$ are coplanar and $n$ is sufficiently large, the total number of planes determined is at least $1 + k \binom{n-k}{2}-\binom{k}{2}(\frac{n-k}{2})$. For similar conditions and sufficiently large $n$, (inspired by the work of P. D. T. A. Elliott in \cite{Ell67}) we also show that the number of spheres determined by $n$ points is at least $1+\binom{n-1}{3}-t_3^{orchard}(n-1)$, and this bound is best possible under its hypothesis. (By $t_3^{orchard}(n)$, we are denoting the maximum number of three-point lines attainable by a configuration of $n$ points, no four collinear, in the plane, i.e., the classic Orchard Problem.) New lower bounds are also given for both lines and circles.Comment: 37 page

First and second variation formulae for the sub-Riemannian area in three-dimensional pseudo-hermitian manifolds

We calculate the first and the second variation formula for the sub-Riemannian area in three dimensional pseudo-hermitian manifolds. We consider general variations that can move the singular set of a C^2 surface and non-singular variation for C_H^2 surfaces. These formulas enable us to construct a stability operator for non-singular C^2 surfaces and another one for C2 (eventually singular) surfaces. Then we can obtain a necessary condition for the stability of a non-singular surface in a pseudo-hermitian 3-manifold in term of the pseudo-hermitian torsion and the Webster scalar curvature. Finally we classify complete stable surfaces in the roto-traslation group RT .Comment: 36 pages. Misprints corrected. Statement of Proposition 9.8 slightly changed and Remark 9.9 adde

Riemannian submersions from almost contact metric manifolds

In this paper we obtain the structure equation of a contact-complex Riemannian submersion and give some applications of this equation in the study of almost cosymplectic manifolds with Kaehler fibres.Comment: Abh. Math. Semin. Univ. Hamb., to appea

Tau-Sleptons and Tau-Sneutrino in the MSSM with Complex Parameters

We present a phenomenological study of tau-sleptons stau_1,2 and tau-sneutrino in the Minimal Supersymmetric Standard Model with complex parameters A_tau, mu and M_1. We analyse production and decays of stau_1,2 and tau-sneutrino at a future e^+ e^- collider. We present numerical predictions for the important decay rates, paying particular attention to their dependence on the complex parameters. The branching ratios of the fermionic decays of stau_1 and tau-sneutrino show a significant phase dependence for tan(beta) < 10. For tan(beta) > 10 the branching ratios for the stau_2 decays into Higgs bosons depend very sensitively on the phases. We show how information on the phase phi(A_tau) and the other fundamental stau parameters can be obtained from measurements of the stau masses, polarized cross sections and bosonic and fermionic decay branching ratios, for small and large tan(beta) values. We estimate the expected errors for these parameters. Given favorable conditions, the error of A_tau is about 10% to 20%, while the errors of the remaining stau parameters are in the range of approximately 1% to 3%. We also show that the induced electric dipole moment of the tau-lepton is well below the current experimental limit.Comment: LaTex, 25 pages, 11 figures (included); v2: extended discussion on error determination, version to appear in Phys.Rev.