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Том 217, № 5 (2016)
- Год: 2016
- Статей: 9
- URL: https://bakhtiniada.ru/1072-3374/issue/view/14766
Article
Conformal Killing Forms on Totally Umbilical Submanifolds
Аннотация
In the present paper we shall study the global existence of conformal Killing forms on compact and orientable submanifolds of pseudo-Riemannian manifolds. In addition, we shall determine exact upper bounds of the dimensions of the vector spaces of these forms on compact and orientable pseudo-Riemannian manifolds.
525-539
Isometries of Spaces with Torsion
Аннотация
In this paper, we study automorphisms (isometries) in Riemann–Cartan spaces (spaces with torsion) of positive definite and alternating Riemannian metrics. We prove that if the connection is semisymmetric, then the maximal dimension of the Lie group of isometries of an n-dimensional space is equal to \( \frac{n\left(n-1\right)}{2}+1 \). If n = 3, then the maximal dimension of the group is equal to 6 and the connection of the maximally movable space is skew symmetric. In this case, the space has a constant curvature k and a constant torsion s, while the Ricci quadratic form is positive (negative) definite if and only if k > s2 (respectively, k < s2) and is equal to zero if k = s2. We construct a maximally movable stationary de Sitter model of the Universe with torsion and propose a geometric interpretation of the torsion of spatial sections.
540-556
Automorphisms of Symplectic and Contact Structures
Аннотация
The survey contains main results of the theory of automorphisms of symplectic (almost symplectic) and contact (almost contact) structures and the original results of the authors of estimates of the maximal dimension of Lie groups of automorphisms of symplectic and contact structures that preserve an associated linear connection.
557-594
Local Structure of Vaisman–Gray Manifolds
Аннотация
In this paper, we introduce the notion of a mapping of adjoint G-structures of almost Hermitian manifolds and obtain relations between components of the fundamental tensor fields of an initial almost Hermitian manifold and the conformally transformed manifold. These formulas are applied to the study of the class of Vaisman–Gray manifolds. We prove that in dimension > 4 the class of Vaisman–Gray manifolds coincides with the class of locally conformally nearly K¨ahlerian manifolds.
595-606
607-623
On the Extendability of Locally Defined Isometries of a Pseudo-Riemannian Manifold
Аннотация
Let η be a stationary subalgebra of the Lie algebra ζ of all Killing vector fields on a pseudo-Riemannian analytic manifold, G be a simply connected Lie group generated by the algebra ζ, and H be its subgroup generated by the subalgebra η. Then the subgroup H is closed in G.
624-627
How to distinguish a mixture of two d-Wave States from a Pure d-Wave State of High-Temperature Superconductors
Аннотация
By the study of the spectrum of collective modes in a pure d-wave state and in a mixed dx2y2 + idxy state of high-temperature superconductors, we show that in spite of the fact that spectra in both pure states dx2y2 and dxy are identical, the spectrum in the mixture dx2y2 + idxy state turns out to be quite different from them. Thus, the probe of the spectrum in ultrasound and/or microwave absorption experiments could be used to distinguish a mixture of two d-wave states from pure d-wave states.
628-638
639-659
Estimates of Quasi-Norms for a Certain Class of Double Sine Series
Аннотация
It this paper, we examine the sums of double sine series with coefficients that are multiply monotonic with respect to subsequences. We obtain sufficient conditions under which these sums belong to the classes Lp, 0 < p < ∞.
660-670