Riemannian manifolds carrying a pair of skew symmetric conformal vector fields

We deal with a Riemannian manifoldM carrying a pair of skew symmetric conformal vector fields (X, Y). The existence of such a pairing is determined by an exterior differential system in involution (in the sense of Cartan). In this case,M is foliated by 3-dimensional totally geodesic submanifolds. Additional geometric properties are proved. Supported by a JSPS postdoctoral fellowship.     

Density of integers which are discriminants of cyclic fields of odd prime degree

An asymptotic formula is given for the number of integers x which are discriminants of cyclic fields of odd prime degree.Received: 17 February 2004     

On Weyl structures

We characterize the relation between the geometrical properties of Weyl manifolds and the algebraic properties of the Weyl algebras (§1) and the deformation algebras associated to two conformal Weyl connections (§2). The last section is devoted to the study of the Weyl-Lyra algebras associated to a conformal Weyl connection and a conformal semisymmetric connection.     

The EC networking on elemental speciation revisited

In Europe, the EC-funded Thematic Network Speciation 21 was instrumental in disseminating the existing knowledge about chemical speciation of trace elements. It created a forum in which analytical chemists working in method development were mixed with potential users from industry and representatives of legislative bodies. This endeavour is continuing in the currently established European Virtual Institute for Speciation Analysis (EVISA). Although there already exists substantial know-how in Europe for the speciation of a number of substances, such as organo-arsenic, organo-tin and organo-mercury compounds, to name just these three groups, there is an urgent need to enforce the analytical potential in speciation analysis on a much wider scope of compounds capable of providing data of a suitable quality. The ensuing need for quality assurance of the analytical procedures requires the analysis of representative reference materials, certified for the relevant species. Last but not least, where applicable, the European-wide legislation should be adapted to focus on toxic species of the elements, rather than the total element.Presented at BERM-9—Ninth International Symposium on Biological and Environmental Reference Materials, June 15–19, 2003, Berlin, Germany. Disclaimer The opinions expressed in the present article are entirely those of the authors. They do not represent the opinion of the European Community.     

Weingarten rotation surfaces in 3-dimensional de Sitter space

In the 3-dimensional de Sitter Space , a surface is said to be a spherical (resp. hyperbolic or parabolic) rotation surface, if it is a orbit of a regular curve under the action of the orthogonal transformations of the 4-dimensional Minkowski space which leave a timelike (resp. spacelike or degenerate) plane pointwise fixed. In this paper, we give all spacelike and timelike Weingarten rotation surfaces in .     

The Yamabe problem for almost Hermitian manifolds

The conformal class of a Hermitian metric g on a compact almost complex manifold (M^2m, J) consists entirely of metrics that are Hermitian with respect to J. For each one of these metrics, we may define a J-twisted version of the Ricci curvature, the J-Ricci curvature, and its corresponding trace, the J-scalar curvature s^J. We ask if the conformal class of g carries a metric with constant s^J, an almost Hermitian version of the usual Yamabe problem posed for the scalar curvature s. We answer our question in the affirmative. In fact, we show that (2m−1)s^J−s=2(2m−1)W(ω, ω), where W is the Weyl tensor and ω is the fundamental form of g. Using techniques developed for the solution of the problem for s, we construct an almost Hermitian Yamabe functional and its corresponding conformal invariant. This invariant is bounded from above by a constant that only depends on the dimension of M, and when it is strictly less than the universal bound, the problem has a solution that minimizes the almost complex Yamabe functional. By the relation above, we see that when W (ω, ω) is negative at least one point, or identically zero, our problem has a solution that minimizes the almost Hermitian Yamabe functional, and the universal bound is reached only in the case of the standard 6-sphere equipped with a suitable almost complex structure. When W(ω, ω) is non-negative and not identically zero, we prove that the conformal invariant is strictly less than the universal bound, thus solving the problem for this type of manifolds as well. We discuss some applications.     

An obstruction to the positivity of relative Yamabe invariants

For a supergroup , we describe an obstruction to the existence of positive scalar curvature metrics with minimal boundary condition on a compact n-dimensional -manifold W with nonempty boundary M, , in terms of the bordism class [M] in the Stolz obstruction group associated to [St2]. In par ticular, when W is a 5-dimensional spin manifold and the -invariant of a connected component of M is nonzero, we prove that W does not admit a positive scalar curvature metric with minimal boundary condition. Received: 4 July 2001; in final form: 5 February 2002 / Published online: 8 November 2002 RID="*" ID="*" Partially supported by the Grants-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, No. 11640070.     

On hypersurfaces inR n+1 with integral bounds on curvature

We show that the L ^p norm of the second fundamental form of hypersurfaces in R ⁿ⁺¹ is very coercive in the GMT setting of Gauss graphs currents, when p exceeds the dimension n. A compactness result for immersed hypersurfaces and its application to a variational problem are provided.     

Lipschitz stability of controlled invariant subspaces

Let (A,B)∈C^n×n×C^n×m and M be an (A, B)-invariant subspace. In this paper the following results are presented: (i) If M∩ImB={0}, necessary and sufficient conditions for the Lipschitz stability of M are given. (ii) If M contains the controllability subspace of the pair (A, B), sufficient conditions for the Lipschitz stability of the subspace M are given.     

The spectrum of semi-Cayley graphs over abelian groups

In this paper, a formula of the spectrum of semi-Cayley graphs over finite abelian groups will be given. In particular, the spectrum of Cayley graphs over dihedral groups and dicyclic groups will be given, respectively.