We prove that the conformal group of a closed, simply connected, real analytic Lorentzian manifold is compact. D’Ambra proved in 1988 isometry such compact [Invent. Math. 92 (1988), pp. 555–565]. Our result implies Lichnerowicz Conjecture for manifolds with finite fundamental group.

The 2-parameter family of certain homogeneous Lorentzian 3-manifolds, which includes Minkowski 3-space and anti-de Sitter 3-space, is considered. Each 3-manifold in the has a solvable Lie group structure with left invariant metric. A generalized integral representation formula for maximal spacelike surfaces 3-manifolds obtained. normal Gauß map its harmonicity are discussed.

We are studying the harmonic and twistor equation on Lorentzian surfaces, that is a two dimensional orientable manifold with a metric of signature (1, 1). We will investigate the properties of the solutions of these equations and try to relate the conformal invariant dimension of the space of harmonic and twistor spinors to the natural conformal invariants given by the Lorentzian metric. We wil...

The holonomy group of an (n+2)–dimensional simply-connected, indecomposable but non-irreducible Lorentzian manifold (M,h) is contained in the parabolic group (R × SO(n)) ⋉ R. The main ingredient of such a holonomy group is the SO(n)–projection G := prSO(n)(Holp(M,h)) and one may ask whether it has to be a Riemannian holonomy group. In this paper we show that this is always the case, completing ...

We investigate the relationship between conformal and spin structure on lorentzian manifolds and see how their compatibility influences the formulation of rigid supersymmetric field theories. In dimensions three, four, six and ten, we show that if the Dirac current associated with a generic spinor defines a null conformal Killing vector then the spinor must obey a twistor equation with respect ...

We consider pointed Lorentzian manifolds and construct “canonical” foliations by constant mean curvature (CMC) hypersurfaces. Our result assumes a uniform bound on the local sup-norm of the curvature of the manifold and on its local injectivity radius, only. The prescribed curvature problem under consideration is a nonlinear elliptic equation whose coefficients have limited regularity. The CMC ...

In this study, some identities involving the Riemannian curvature invariants are presented on lightlike hypersurfaces of a statistical manifold in Lorentzian settings. Several inequalities characterizing obtained. These also investigated space forms.