Semisymmetry and Ricci-symmetry for Hypersurfaces of Semi-euclidean Spaces
We determine in the form of curves corresponding to strictly monotone functions as well as the components of affine connections for which any image of under a compact-free group of affinities containing the translation group is a geodesic with respect to . Special attention is paid to the case that contains many dilatations or that is a curve in . If is a curve in and is the translation group then we calculate not only the components of the curvature and the Weyl tensor but...
Given a finite additive abelian group and an integer , with , denote by the simple incidence structure whose point-set is and whose blocks are the -subsets of such that . It is known (see [Caggegi, A., Di Bartolo, A., Falcone, G.: Boolean 2-designs and the embedding of a 2-design in a group arxiv 0806.3433v2, (2008), 1–8.]) that is a 2-design, if is an elementary abelian -group with a prime divisor of . From [Caggegi, A., Falcone, G., Pavone, M.: On the additivity of block...
A Walker 4-manifold is a pseudo-Riemannian manifold (M₄,g) of neutral signature, which admits a field of parallel null 2-planes. We study almost paracomplex structures on 4-dimensional para-Kähler-Walker manifolds. In particular, we obtain conditions under which these almost paracomplex structures are integrable, and the corresponding para-Kähler forms are symplectic. We also show that Petean's example of a nonflat indefinite Kähler-Einstein 4-manifold is a special case of our constructions.
We focus our attention on projectively flat affine surfaces. First, we classify the affine surfaces with projectively flat induced connection and constant Pick invariant. We also investigate the compact case and study how the geometry at the boundary determines the geometry of the surface.
In this paper, we get an intrinsic inequality for spacelike submanifolds in indefinite space form , . We also get some rigidity theorems for such spacelike submanifolds.
On any space-like Weingarten surface in the three-dimensional Minkowski space we introduce locally natural principal parameters and prove that such a surface is determined uniquely up to motion by a special invariant function, which satisfies a natural non-linear partial differential equation. This result can be interpreted as a solution to the Lund-Regge reduction problem for space-like Weingarten surfaces in Minkowski space. We apply this theory to linear fractional space-like Weingarten surfaces...
This work is devoted to the study of Einstein equations with a special shape of the energy-momentum tensor. Our results continue Stepanov’s classification of Riemannian manifolds according to special properties of the energy-momentum tensor to Kähler manifolds. We show that in this case the number of classes reduces.
In this paper, we study the stability of space-like hypersurfaces with constant scalar curvature immersed in the de Sitter spaces.