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1
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Osculating curves in 4-dimensional semi-Euclidean space with index 2

100%
İlarslan K., Kiliç N., Erdem H. A.
Open Mathematics
|
2017
|
tom 15
|
nr 1
562-567
EN
In this paper, we give the necessary and sufficient conditions for non-null curves with non-null normals in 4-dimensional Semi-Euclidian space with indeks 2 to be osculating curves. Also we give some examples of non-null osculating curves in [...] E24 $\mathbb{E}_{2}^{4}$ .
2
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Complete classification of parallel Lorentz surfaces in neutral pseudo hyperbolic 4-space

76%
Chen B.-Y.
Open Mathematics
|
2010
|
tom 8
|
nr 4
706-734
EN
A Lorentz surface of an indefinite space form is called a parallel surface if its second fundamental form is parallel with respect to the Van der Waerden-Bortolotti connection. Such surfaces are locally invariant under the reflection with respect to the normal space at each point. Parallel surfaces are important in geometry as well as in general relativity since extrinsic invariants of such surfaces do not change from point to point. Recently, parallel Lorentz surfaces in 4D neutral pseudo Euclidean 4-space $$ \mathbb{E}_2^4 $$ and in neutral pseudo 4-sphere S 24 (1) were classified in [14] and in [10], respectively. In this paper, we completely classify parallel Lorentz surfaces in neutral pseudo hyperbolic 4-space H 24 (−1). Our main result states that there are 53 families of parallel Lorentz surfaces in H 24 (−1). Conversely, every parallel Lorentz surface in H 24 (−1) is obtained from the 53 families. As an immediate by-product, we achieve the complete classification of all parallel Lorentz surfaces in 4D neutral indefinite space forms.
3
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On canonical screen for lightlike submanifolds of codimension two

76%
Duggal K.
Open Mathematics
|
2007
|
tom 5
|
nr 4
710-719
EN
In this paper we study two classes of lightlike submanifolds of codimension two of semi-Riemannian manifolds, according as their radical subspaces are 1-dimensional or 2-dimensional. For a large variety of both these classes, we prove the existence of integrable canonical screen distributions subject to some reasonable geometric conditions and support the results through examples.
4
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A classification of the torsion tensors on almost contact manifolds with B-metric

76%
Manev M., Ivanova M.
Open Mathematics
|
2014
|
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.
5
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Complete classification of spatial surfaces with parallel mean curvature vector in arbitrary non-flat pseudo-Riemannian space forms

76%
Chen B.-Y.
Open Mathematics
|
2009
|
tom 7
|
nr 3
400-428
EN
Submanifolds with parallel mean curvature vector play important roles in differential geometry, theory of harmonic maps as well as in physics. Spatial surfaces in 4D Lorentzian space forms with parallel mean curvature vector were classified by B. Y. Chen and J. Van der Veken in [9]. Recently, spatial surfaces with parallel mean curvature vector in arbitrary pseudo-Euclidean spaces are also classified in [7]. In this article, we classify spatial surfaces with parallel mean curvature vector in pseudo-Riemannian spheres and pseudo-hyperbolic spaces with arbitrary codimension and arbitrary index. Consequently, we achieve the complete classification of spatial surfaces with parallel mean curvature vector in all pseudo-Riemannian space forms. As an immediate by-product, we obtain the complete classifications of spatial surfaces with parallel mean curvature vector in arbitrary Lorentzian space forms.
6
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Einstein-Weyl structures on lightlike hypersurfaces

76%
Atindogbe C., Bérard-Bergery L., Ogouyandjou C.
Open Mathematics
|
2013
|
tom 11
|
nr 10
1850-1862
EN
We study Weyl structures on lightlike hypersurfaces endowed with a conformal structure of certain type and specific screen distribution: the Weyl screen structures. We investigate various differential geometric properties of Einstein-Weyl screen structures on lightlike hypersurfaces and show that, for ambient Lorentzian space ℝ1n+2 and a totally umbilical screen foliation, there is a strong interplay with the induced (Riemannian) Weyl-structure on the leaves.
7
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On the Ricci operator of locally homogeneous Lorentzian 3-manifolds

76%
Calvaruso G., Kowalski O.
Open Mathematics
|
2009
|
tom 7
|
nr 1
124-139
EN
We determine the admissible forms for the Ricci operator of three-dimensional locally homogeneous Lorentzian manifolds.
8
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On conformally flat Lorentz parabolic manifolds

64%
Kamishima Y.
Open Mathematics
|
2014
|
tom 12
|
nr 6
861-878
EN
We introduce conformally flat Fefferman-Lorentz manifold of parabolic type as a special class of Lorentz parabolic manifolds. It is a smooth (2n+2)-manifold locally modeled on (Û(n+1, 1), S 2n+1,1). As the terminology suggests, when a Fefferman-Lorentz manifold M is conformally flat, M is a Fefferman-Lorentz manifold of parabolic type. We shall discuss which compact manifolds occur as a conformally flat Fefferman-Lorentz manifold of parabolic type.
9
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Curvature properties of φ-null Osserman Lorentzian S-manifolds

64%
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.
10
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Foliations of lightlike hypersurfaces and their physical interpretation

64%
Duggal K.
Open Mathematics
|
2012
|
tom 10
|
nr 5
1789-1800
EN
This paper deals with a family of lightlike (null) hypersurfaces (H u) of a Lorentzian manifold M such that each null normal vector ℓ of H u is not entirely in H u, but, is defined in some open subset of M around H u. Although the family (H u) is not unique, we show, subject to some reasonable condition(s), that the involved induced objects are independent of the choice of (H u) once evaluated at u = constant. We use (n+1)-splitting Lorentzian manifold to obtain a normalization of ℓ and a well-defined projector onto H, needed for Gauss, Weingarten, Gauss-Codazzi equations and calculate induced metrics on proper totally umbilical and totally geodesic H u. Finally, we establish a link between the geometry and physics of lightlike hypersurfaces and a variety of black hole horizons.
11
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Harmonicity of vector fields on four-dimensional generalized symmetric spaces

64%
Calvaruso G.
Open Mathematics
|
2012
|
tom 10
|
nr 2
411-425
EN
Let (M = G/H;g)denote a four-dimensional pseudo-Riemannian generalized symmetric space and g = m + h the corresponding decomposition of the Lie algebra g of G. We completely determine the harmonicity properties of vector fields belonging to m. In some cases, all these vector fields are critical points for the energy functional restricted to vector fields. Vector fields defining harmonic maps are also classified, and the energy of these vector fields is explicitly calculated.
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