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Shells of monotone curves

Josef Mikeš, Karl Strambach (2015)

Czechoslovak Mathematical Journal

We determine in ℝ n the form of curves C corresponding to strictly monotone functions as well as the components of affine connections ∇ for which any image of C under a compact-free group Ω of affinities containing the translation group is a geodesic with respect to ∇ . Special attention is paid to the case that Ω contains many dilatations or that C is a curve in ℝ 3 . If C is a curve in ℝ 3 and Ω is the translation group then we calculate not only the components of the curvature and the Weyl tensor but...

Some Additive 2 - ( v , 5 , λ ) Designs

Andrea Caggegi (2015)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Given a finite additive abelian group G and an integer k , with 3 ≤ k ≤ | G | , denote by 𝒟 k ( G ) the simple incidence structure whose point-set is G and whose blocks are the k -subsets C = { c 1 , c 2 , ⋯ , c k } of G such that c 1 + c 2 + ⋯ + c k = 0 . 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 𝒟 k ( G ) is a 2-design, if G is an elementary abelian p -group with p a prime divisor of k . From [Caggegi, A., Falcone, G., Pavone, M.: On the additivity of block...

Some properties of para-Kähler-Walker metrics

Mustafa Özkan, Murat İşcan (2014)

Annales Polonici Mathematici

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.

Some results on projectively flat affine surfaces

Antonio Martínez, Francisco Milán (2005)

Banach Center Publications

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.

Space-like Weingarten surfaces in the three-dimensional Minkowski space and their natural partial differential equations

Georgi Ganchev, Vesselka Mihova (2013)

Open Mathematics

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...

Special Einstein’s equations on Kähler manifolds

Irena Hinterleitner, Volodymyr Kiosak (2010)

Archivum Mathematicum

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.

Currently displaying 181 – 200 of 258