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Semiparallel isometric immersions of 3-dimensional semisymmetric Riemannian manifolds

Ülo Lumiste (2003)

Czechoslovak Mathematical Journal

A Riemannian manifold is said to be semisymmetric if R ( X , Y ) · R = 0 . A submanifold of Euclidean space which satisfies R ¯ ( X , Y ) · h = 0 is called semiparallel. It is known that semiparallel submanifolds are intrinsically semisymmetric. But can every semisymmetric manifold be immersed isometrically as a semiparallel submanifold? This problem has been solved up to now only for the dimension 2, when the answer is affirmative for the positive Gaussian curvature. Among semisymmetric manifolds a special role is played by the foliated...

Semi-symmetric 𝔓 -spaces

Eric Boeckx (1994)

Commentationes Mathematicae Universitatis Carolinae

We determine explicitly the local structure of a semi-symmetric 𝔓 -space.

Shells of monotone curves

Josef Mikeš, Karl Strambach (2015)

Czechoslovak Mathematical Journal

We determine in 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 3 . If C is a curve in 3 and Ω is the translation group then we calculate not only the components of the curvature and the Weyl tensor but...

Slant and Legendre curves in Bianchi-Cartan-Vranceanu geometry

Constantin Călin, Mircea Crasmareanu (2014)

Czechoslovak Mathematical Journal

We study Legendre and slant curves for Bianchi-Cartan-Vranceanu metrics. These curves are characterized through the scalar product between the normal at the curve and the vertical vector field and in the helix case they have a proper (non-harmonic) mean curvature vector field. The general expression of the curvature and torsion of these curves and the associated Lancret invariant (for the slant case) are computed as well as the corresponding variant for some particular cases. The slant (particularly...

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...

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