Filip Defever

On ricci-pseudosymmetric hypersurfaces in spaces of constant curvature

This article studies the conditions of pseudosymmetry and Ricci-pseudosymmetry, realizedon hypersurfaces of semi-Riemannian spaces of constant curvature. In particular, we derive extrinsic characterizations of pseudosymmetric and Ricci-pseudosymmetric hypersurfaces of semi-Riemannian spaces of constant curvature in terms of the shape operator. As an application, and in the Riemannian case, we extend a theorem by K. Nomizu on semisymmetric hypersurfaces of Euclidean spaces.

On pseudosymmetric space–times

An algebraic classification of four‐dimensional pseudosymmetric Einstein space–times is given and more examples of pseudosymmetric space–times are provided.

P.J. Ryan's problem in semi-Riemannian space forms

We prove that the conditions R · R =0 and R · S =0 are equivalent for hypersurfaces of a 5-dimensional semi-Riemannian space form N 5 ( c ). This solves a problem by P.J. Ryan in the case of hypersurfaces of dimension 4 in semi-Riemannian space forms.

Superconformal algebras with quadratic nonlinearity

Abstract We present new superconformal algebras, containing both bosonic and fermionic supersymmetries, based on the superalgebras OSp(m|2n) and U(m|n). They contain as special cases the previously known series based on O( m ), U( m ) and Sp(2 n ) Lie algebras. The case U(n+2|n) is special, in that it can be reduced to SU(n+2|n), generalising the standard N = 4 superconformal algebra.

Nonassociative superconformal algebras

A study of conventional superconformal not‐necessarily Lie superalgebras is performed. A uniform prescription is given, leading to the definition of a family of structures with N=1,...,8 supersymmetries. For N≤4, Lie superalgebras are recovered, for N≥5 the algebras are nonassociative. The not‐Lie superconformal algebras with N=5,6,7,8 share interesting common properties, relating them to the Cayley numbers, covariant derivation of spinors on the seven‐sphere S7 and torsions on supercoset manifolds. The N=8 case is related to the (soft) constraint algebra of a recent reformulation of the Green’s–Schwarz superstring.

A BOSONIC MODEL FOR PARTICLES WITH ARBITRARY SPIN

We formulate a simple classical model without Grassmann variables. Quantization of this model gives a unified quantum-mechanical description for massive and massless particles of arbitrary spin and helicity. In the phase space of the classical model a “bosonic” version of the super-Poincare algebra is realized. At the quantum level it generates the spectrum of the model.

A note on almost kähler manifolds

For anyn ≥ 2, we give examples of almost Kähler conformally flat manifoldsM2n which are not Kähler. We discuss the meaning of these examples in the context of the Goldberg conjecture on almost Kahler manifolds.

Conformally flat hypersurfaces of E4 with constant mean curvature

We consider 3-dimensional conformally flat hypersurfaces of E4 with constant mean curvature; we prove that the ones with 3 different principal curvatures must necessarilly be minimal.

The compact cyclides of Dupin and a conjecture of B.-Y. Chen

We show that the compact cyclides of Dupin are of infinite type; this result provides further support for a conjecture of Chen.

Superconformal algebras with N=5, 6, 7, 8. I

The authors define a family of four superconformal nonLie superalgebras with N=5, 6, 7, 8 supersymmetries. An interpretation is given, relating them to covariant derivation of spinors on the 7-sphere S7.