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Invariant almost contact structure on the real extension of a sphere
Учёные записки Казанского университета: Серия Физико-математические наукиThe existence of contact and almost contact metric structures invariant under the group of motions on the real extension of a two-dimensional sphere with a Riemannian direct product metric was examined.
M. V. Sorokina, Y. V. Morshchinkina
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Weak Quasi-Contact Metric Manifolds and New Characteristics of K-Contact and Sasakian Manifolds
MathematicsQuasi-contact metric manifolds (introduced by Y. Tashiro and then studied by several authors) are a natural extension of contact metric manifolds. Weak almost-contact metric manifolds, i.e., where the linear complex structure on the contact distribution ...
Vladimir Rovenski
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Matrix Lie groups as 3-dimensional almost contact B-metric manifolds [PDF]
, 2015 The object of investigation are Lie groups considered as almost contact B-metric manifolds of the lowest dimension three. It is established a correspondence of all basic-class-manifolds of the Ganchev-Mihova-Gribachev classification of the studied ...
Manev, Hristo
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Geometric structures on loop and path spaces
, 2010 Is is known that the loop space associated to a Riemannian manifold admits a quasi-symplectic structure. This article shows that this structure is not likely to recover the underlying Riemannian metric by proving a result that is a strong indication of ...
A. Pressley +6 more
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A dimensional restriction for a class of contact manifolds
Demonstratio Mathematica, 2017 In this work we consider a class of contact manifolds (M, η) with an associated almost contact metric Structure (ϕ, ξ, η, g). This class contains, for example, nearly cosymplectic manifolds and the manifolds in the class C9 ⊕ C10 defined by Chinea and ...
Loiudice Eugenia
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On transversally elliptic operators and the quantization of manifolds with $f$-structure
, 2011 An $f$-structure on a manifold $M$ is an endomorphism field $\phi\in\Gamma(M,\End(TM))$ such that $\phi^3+\phi=0$. Any $f$-structure $\phi$ determines an almost CR structure $E_{1,0}\subset T_\C M$ given by the $+i$-eigenbundle of $\phi$.
D. E. Blair +15 more
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Three-dimensional homogeneous almost contact metric structures
Journal of Geometry and Physics, 2013 A manifold \(M^{2n+1}\) is said to be almost contact if its structure group can be reduced to \(\mathrm U(n)\). Equivalently, this means that \(M\) admits an almost contact structure, that is, a triple \((\varphi, \xi, \eta)\), where \(\varphi\) is a (1,1)-tensor, \(\xi\) a global vector field and \(\eta\) a 1-form, such that \(\varphi(\xi ) = 0 ...
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Sewing cells in almost cosymplectic and almost Kenmotsu geometry [PDF]
, 2012 For a finite family of 3-dimensional almost contact metric manifolds with closed the structure form $\eta$ is described a construction of an almost contact metric manifold, where the members of the family are building blocks - cells.
Dacko, Piotr
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Almost Contact Metric Structures Defined by a Symplectic Structure Over a Distribution
Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics, 2015 Summary: The distribution \(D\) of an almost contact metric structure \((\varphi, \vec \xi, \eta, g)\) is an odd analogue of the tangent bundle. In the paper an intrinsic symplectic structure naturally associated with the initial almost contact metric structure is constructed. The interior connection defines the parallel transport of admissible vectors
Galaev, S. V., Shevtsova, Yu. V.
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On the geometry of generalized nonholonomic Kenmotsu manifolds
Дифференциальная геометрия многообразий фигур, 2022 The concept of a generalized nonholonomic Kenmotsu manifold is introduced. In contrast to the previously defined nonholonomic Kenmotsu manifold, the manifold studied in the article is an almost normal almost contact metric manifold of odd rank.
A.V. Bukusheva
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