Displaying similar documents to “Some special geometry in dimension six”

On the normality of an almost contact 3 -structure on Q R -submanifolds

Shoichi Funabashi, Jin Suk Pak, Yang Jae Shin (2003)

Czechoslovak Mathematical Journal

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We study n -dimensional Q R -submanifolds of Q R -dimension ( p - 1 ) immersed in a quaternionic space form Q P ( n + p ) / 4 ( c ) , c ≧ 0 , and, in particular, determine such submanifolds with the induced normal almost contact 3 -structure.

On almost cosymplectic (κ,μ,ν)-spaces

Piotr Dacko, Zbigniew Olszak (2005)

Banach Center Publications

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An almost cosymplectic (κ,μ,ν)-space is by definition an almost cosymplectic manifold whose structure tensor fields φ, ξ, η, g satisfy a certain special curvature condition (see formula (eq1b)). This condition is invariant with respect to the so-called -homothetic transformations of almost cosymplectic structures. For such manifolds, the tensor fields φ, h ( = ( 1 / 2 ) ℒ ξ φ ), A ( = -∇ξ) fulfill a certain system of differential equations. It is proved that the leaves of the canonical foliation of an...

Remarks on CR-manifolds of codimension 2 in C 4

Schmalz, Gerd

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The aim of the article is to give a conceptual understanding of Kontsevich’s construction of the universal element of the cohomology of the coarse moduli space of smooth algebraic curves with given genus and punctures. In a first step the author presents a toy model of tree graphs coloured by an operad 𝒫 for which the graph complex and the universal cycle will be constructed. The universal cycle has coefficients in the operad for Ω ( 𝒫 * ) -algebras with trivial differential over the (dual) cobar...

On torsion of a 3 -web

Alena Vanžurová (1995)

Mathematica Bohemica

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A 3-web on a smooth 2 n -dimensional manifold can be regarded locally as a triple of integrable n -distributions which are pairwise complementary, [5]; that is, we can work on the tangent bundle only. This approach enables us to describe a 3 -web and its properties by invariant ( 1 , 1 ) -tensor fields P and B where P is a projector and B 2 = id. The canonical Chern connection of a web-manifold can be introduced using this tensor fields, [1]. Our aim is to express the torsion tensor T of the Chern connection...

Vanishing conharmonic tensor of normal locally conformal almost cosymplectic manifold

Farah H. Al-Hussaini, Aligadzhi R. Rustanov, Habeeb M. Abood (2020)

Commentationes Mathematicae Universitatis Carolinae

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The main purpose of the present paper is to study the geometric properties of the conharmonic curvature tensor of normal locally conformal almost cosymplectic manifolds (normal LCAC-manifold). In particular, three conhoronic invariants are distinguished with regard to the vanishing conharmonic tensor. Subsequentaly, three classes of normal LCAC-manifolds are established. Moreover, it is proved that the manifolds of these classes are η -Einstein manifolds of type ( α , β ) . Furthermore, we have...