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1
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Paraquaternionic CR-submanifolds of paraquaternionic Kähler manifolds and semi-Riemannian submersions

100%
Ianuş S., Marchiafava S., Vîlcu G.
Open Mathematics
|
2010
|
tom 8
|
nr 4
735-753
EN
In this paper we introduce paraquaternionic CR-submanifolds of almost paraquaternionic hermitian manifolds and state some basic results on their differential geometry. We also study a class of semi-Riemannian submersions from paraquaternionic CR-submanifolds of paraquaternionic Kähler manifolds.
2
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Total curvature and volume of foliations on the sphere S 2

81%
Fawaz A.
Open Mathematics
|
2009
|
tom 7
|
nr 4
660-669
EN
In this paper we study a curvature integral associated with a pair of orthogonal foliations on the Riemann sphere S 2 and we compute the minimal value of the volume of meromorphic foliations.
3
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Real hypersurfaces in complex two-plane Grassmannians whose normal Jacobi operator is of Codazzi type

81%
Machado C., Dios Pérez J., Jeong I., Suh Y.
Open Mathematics
|
2011
|
tom 9
|
nr 3
578-582
EN
We prove the non-existence of real hypersurfaces in complex two-plane Grassmannians whose normal Jacobi operator is of Codazzi type.
4
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Free CR distributions

81%
Schmalz G., Slovák J.
Open Mathematics
|
2012
|
tom 10
|
nr 5
1896-1913
EN
There are only some exceptional CR dimensions and codimensions such that the geometries enjoy a discrete classification of the pointwise types of the homogeneous models. The cases of CR dimensions n and codimensions n 2 are among the very few possibilities of the so-called parabolic geometries. Indeed, the homogeneous model turns out to be PSU(n+1,n)/P with a suitable parabolic subgroup P. We study the geometric properties of such real (2n+n 2)-dimensional submanifolds in $\mathbb{C}^{n + n^2 } $ for all n > 1. In particular, we show that the fundamental invariant is of torsion type, we provide its explicit computation, and we discuss an analogy to the Fefferman construction of a circle bundle in the hypersurface type CR geometry.
5
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On the structure vector field of a real hypersurface in complex two-plane Grassmannians

81%
Machado C., Pérez J.
Open Mathematics
|
2012
|
tom 10
|
nr 2
451-455
EN
Considering the notion of Jacobi type vector fields for a real hypersurface in a complex two-plane Grassmannian, we prove that if a structure vector field is of Jacobi type it is Killing. As a consequence we classify real hypersurfaces whose structure vector field is of Jacobi type.
6
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Harmonic conformal flows on manifolds of constant curvature

81%
Fawaz A.
Open Mathematics
|
2007
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tom 5
|
nr 3
493-504
EN
We compute the energy of conformal flows on Riemannian manifolds and we prove that conformal flows on manifolds of constant curvature are critical if and only if they are isometric.
7
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Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster $$\mathfrak{D}^ \bot$$-parallel structure Jacobi operator

81%
Pak E., Suh Y.
Open Mathematics
|
2014
|
tom 12
|
nr 12
1840-1851
EN
Regarding the generalized Tanaka-Webster connection, we considered a new notion of $$\mathfrak{D}^ \bot$$-parallel structure Jacobi operator for a real hypersurface in a complex two-plane Grassmannian G 2(ℂm+2) and proved that a real hypersurface in G 2(ℂm+2) with generalized Tanaka-Webster $$\mathfrak{D}^ \bot$$-parallel structure Jacobi operator is locally congruent to an open part of a tube around a totally geodesic quaternionic projective space ℍP n in G 2(ℂm+2), where m = 2n.
8
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A classification of the torsion tensors on almost contact manifolds with B-metric

62%
Manev M., Ivanova M.
Open Mathematics
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2014
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tom 12
|
nr 10
1416-1432
EN
The space of the torsion (0,3)-tensors of the linear connections on almost contact manifolds with B-metric is decomposed in 15 orthogonal and invariant subspaces with respect to the action of the structure group. Three known connections, preserving the structure, are characterized regarding this classification.
9
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On Galilean connections and the first jet bundle

62%
Grant J., Lackey B.
Open Mathematics
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2012
|
tom 10
|
nr 5
1889-1895
EN
We see how the first jet bundle of curves into affine space can be realized as a homogeneous space of the Galilean group. Cartan connections with this model are precisely the geometric structure of second-order ordinary differential equations under time-preserving transformations - sometimes called KCC-theory. With certain regularity conditions, we show that any such Cartan connection induces “laboratory” coordinate systems, and the geodesic equations in this coordinates form a system of second-order ordinary differential equations. We then show the converse - the “fundamental theorem” - that given such a coordinate system, and a system of second order ordinary differential equations, there exists regular Cartan connections yielding these, and such connections are completely determined by their torsion.
10
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Anti-invariant Riemannian submersions from almost Hermitian manifolds

62%
Ṣahin B.
Open Mathematics
|
2010
|
tom 8
|
nr 3
437-447
EN
We introduce anti-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. We give an example, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and check the harmonicity of such submersions. We also find necessary and sufficient conditions for a Langrangian Riemannian submersion, a special anti-invariant Riemannian submersion, to be totally geodesic. Moreover, we obtain decomposition theorems for the total manifold of such submersions.
11
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Commuting Conditions of the k-th Cho operator with the structure Jacobi operator of real hypersurfaces in complex space forms

62%
Panagiotidou K., Pérez J. d. D.
Open Mathematics
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2015
|
tom 13
|
nr 1
EN
In this paper three dimensional real hypersurfaces in non-flat complex space forms whose k-th Cho operator with respect to the structure vector field ξ commutes with the structure Jacobi operator are classified. Furthermore, it is proved that the only three dimensional real hypersurfaces in non-flat complex space forms, whose k-th Cho operator with respect to any vector field X orthogonal to structure vector field commutes with the structure Jacobi operator, are the ruled ones. Finally, results concerning real hypersurfaces in complex hyperbolic space satisfying the above conditions are also provided.
12
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A non-homogeneous, symmetric contact projective structure

62%
Zalabová L.
Open Mathematics
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2014
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tom 12
|
nr 6
879-886
EN
We construct a non-homogeneous contact projective structure which is symmetric from the point of view of parabolic geometries.
13
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Formality and the Lefschetz property in symplectic and cosymplectic geometry

52%
Bazzoni G., Fernández M., Muñoz V.
Complex Manifolds
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2015
|
tom 2
|
nr 1
EN
We review topological properties of Kähler and symplectic manifolds, and of their odd-dimensional counterparts, coKähler and cosymplectic manifolds. We focus on formality, Lefschetz property and parity of Betti numbers, also distinguishing the simply-connected case (in the Kähler/symplectic situation) and the b1 = 1 case (in the coKähler/cosymplectic situation).
14
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Curvature properties of φ-null Osserman Lorentzian S-manifolds

52%
Brunetti L., Caldarella A.
Open Mathematics
|
2014
|
tom 12
|
nr 1
97-113
EN
We expound some results about the relationships between the Jacobi operators with respect to null vectors on a Lorentzian S-manifold and the Jacobi operators with respect to particular spacelike unit vectors. We study the number of the eigenvalues of such operators on Lorentzian S-manifolds satisfying the φ-null Osserman condition, under suitable assumptions on the dimension of the manifold. Then, we provide in full generality a new curvature characterization for Lorentzian S-manifolds and we use it to obtain an algebraic decomposition for the Riemannian curvature tensor of φ-null Osserman Lorentzian S-manifolds.
15
Content available remote

On localization in holomorphic equivariant cohomology

43%
Bruzzo U., Rubtsov V.
Open Mathematics
|
2012
|
tom 10
|
nr 4
1442-1454
EN
We study a holomorphic equivariant cohomology built out of the Atiyah algebroid of an equivariant holomorphic vector bundle and prove a related localization formula. This encompasses various residue formulas in complex geometry, in particular we shall show that it contains as special cases Carrell-Liebermann’s and Feng-Ma’s residue formulas, and Baum-Bott’s formula for the zeroes of a meromorphic vector field.
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