Generation of accurate Einstein-equation solutions by five-dimensional rotations

Spherically symmetric solutions of the combined system of four-dimensional Einstein, Maxwell, and specific scalar-field equations are obtained by generalization of the Schwarzschild metric and its subsequent linear quasi-rotation in the (x⁰, x⁵) plane. The accurate Kramer—Legkii solution of the five-dimensional Einstein equations is used. New accurate solutions generalizing the well-known Reissner—Nordstrom and Fisher metrics are obtained.K. D. Ushinskii Yaroslav State Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 22–25, October, 1994.     

On the Curvature of Kähler Manifolds with Zero Ricci Tensor

Mathematical Notes - The behavior of the modulus of the curvature tensor and of the holomorphic sectional curvature on Ricci-flat Kähler manifolds is investigated.     

4D Homogeneous Isotropic Cosmological Models Generated by the 5D Vacuum

4-Dimensional homogeneous isotropic cosmological models obtained from solutions of vacuum 5-dimensional Einstein equations are considered. It is assumed, that the G₅₅-component of the 5D metric simulates matter in the comoving frame of reference. The observable 4D metric is defined up to conformal transformations of the metric of the 4D section g, with a conformal factor as a function of the component G₅₅. It is demonstrated, that the form of this function determines the matter equation of state. Possible equations of state are analyzed separately for flat, open and closed models.     

Generalization of the Bohlin–Arnold Theorem and Its Application in General Relativity Theory

The general Bohlin transforms are used to switch between the solutions of the problem on the motion of a test body with different spherically symmetric potentials. It has been established that the parabolic Bohlin transforms are grouped in character. The Bohlin transforms describing the change from a simple exponential potential to a generalized polynomial potential have been obtained in the general form. With specific, widely known spherically symmetric metrics used as an example, it has been shown that these transforms can be used to determine the trajectory of a test body in general relativity theory.     

Nematic Structure of Space-Time and Its Topological Defects in 5D Kaluza-Klein Theory

We show, that classical Kaluza-Klein theory possesses hidden nematic dynamics. It appears as a consequence of 1+4-decomposition procedure, involving 4D observers 1-form . After extracting of boundary terms the, so called, effective matter part of 5D geometrical action becomes proportional to the square of the anholonomicity 3-form d. It can be interpreted as twist nematic elastic energy, responsible for elastic reaction of 5D space-time on presence of anholonomic 4D submanifold, defined by . We derive both 5D covariant and 1+4 forms of the 5D nematic equilibrium equations, consider simple examples and discuss some 4D physical aspects of generic 5D nematic topological defects.     

Quasi-linear elliptic differential equations for mappings of manifolds,II

We study questions related to the orientability of the infinite-dimensional moduli spaces formed by solutions of elliptic equations for mappings of manifolds. The principal result states that the first Stiefel–Whitney class of such a moduli space is given by the ℤ₂-spectral flow of the families of linearised operators. Under an additional compactness hypotheses, we develop elements of Morse–Bott theory and express the algebraic number of solutions of a non-homogeneous equation with a generic right-hand side in terms of the Euler characteristic of the space of solutions corresponding to the homogeneous equation. The applications of this include estimates for the number of homotopic maps with prescribed tension field and for the number of the perturbed pseudoholomorphic tori, sharpening some known results. Mathematics Subject Classifications (2000): 35J05, 58B15, 58E05, 58E20, 53D45     

Variational aspects of Laplace eigenvalues on Riemannian surfaces

We study the existence and properties of metrics maximising the first Laplace eigenvalue among conformal metrics of unit volume on Riemannian surfaces. We describe a general approach to this problem and its higher eigenvalue versions via the direct method of calculus of variations. The principal results include the general regularity properties of _λk${\lambda }_k$-extremal metrics and the existence of a partially regular _λ1${\lambda }_1$-maximiser.     

Molecular structure of o-chlorphenyldichlorarsine o-ClC6H4AsCl2 using data from gas phase electron diffraction and vibration spectroscopy

A. E. Arbuzov Institute of Organic and Physical Chemistry, Kazan Branch, Academy of Sciences of the USSR. Translated from Zhurnal Strukturnoi Khimii, Vol. 29, No. 4, pp. 64–69, July–August, 1988.     

Imitation of matter by a scalar field in five-dimensional Kaluza-Klein theory

The interpretation of the scalar field ={ie96-1} in the five-dimensional variant of Kaluza-Klein theory is considered. It is proposed that the scalar field be considered as the generalized potential of four material velocities. It can be shown that with additional limitations on the scalar field the right side of the split five-dimensional Einstein equations transform to a hydrodynamic energy-momentum tensor for an ideal liquid with a limited set of equations of state. Concrete five-dimensional metrics, which are obligatorily nonstationary, are analyzed from this viewpoint.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 111–117, January, 1995.