On Some Ricci-Flat Metrics of Cohomogeneity Two on Complex Line Bundles

We construct a family of four-dimensional smooth Ricci-flat Riemann orbifolds of cohomogeneity two which possess the structure of complex line bundles.     

On the new examples of complete noncompact Spin(7)-holonomy metrics

We construct some complete Spin(7)-holonomy Riemannian metrics on the noncompact orbifolds that are ?⁴-bundles with an arbitrary 3-Sasakian spherical fiber M. We prove the existence of the smooth metrics for M = S ⁷ and M = SU(3)/U(1) which were found earlier only numerically.     

Laws of electrical stimulation of plastic deformation of metals and alloys at various structural levels

The laws governing the electrical stimulation of plastic deformation at various structural levels are reviewed. The following topics are covered: the hierarchy of external current stimuli affecting plastic deformation; the variation of the mobility of individual dislocations in zones of thermally activated and quasiviscous motion associated with mechanical, electrical, and combined stimuli over a wide range of temperatures (microlevel); the evolution of defect structure in materials of various structural classes subjected to electrical stimulation over a wide range of strains (mesolevel); the ordered character of plastic deformation inhomogeneities; models of the stress — strain state in the presence of current stimulation (macrolevel) and their interpretation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 66–96, March, 1996.     

<Emphasis Type="Italic">G</Emphasis><Subscript>2</Subscript>-holonomy metrics connected with a 3-Sasakian manifold

We construct complete noncompact Riemannian metrics with G ₂-holonomy on noncompact orbifolds that are ?³-bundles with the twistor space Open image in new window as a spherical fiber.     

Stress-strain state of a circular diaphragm in dynamics

The study of the deformation of diaphragms by impulsive loadings is an urgent problem in view of the more and more widely used techniques of high-speed forming of sheet materials (hydroexplosive, electromagnetic, and electrohydraulic stamping). A number of papers [1, 2] have appeared on the dynamics of the deformation of elastic diaphragms. Problems of axisymmetric plastic flow under pulsed loading have been studied by the method of characteristics [3, 4]. Important applied aspects of explosive loading of diaphragms are described in [5]. We discuss the dependence of the properties of a transverse plastic wave (distortion wave) in a diaphragm on the state of stress. The motion is analyzed in an approximate formulation neglecting radial displacements along the Eulerian coordinate and the change in thickness of the diaphragm. The diaphragm material satisfies the Treska — Saint Venant yield condition. Results of experiments on hydroexplosively loaded diaphragms are presented.     

Noncompact Riemannian spaces with the holonomy group spin(7) and 3-Sasakian manifolds

We complete the study of the existence of Riemannian metrics with Spin(7) holonomy that smoothly resolve standard cone metrics on noncompact manifolds and orbifolds related to 7-dimensional 3-Sasakian spaces.     

On the four-dimensional T<Superscript>2</Superscript>-manifolds of positive Ricci curvature

We prove that there is a T ²-invariant Riemannian metric of positive Ricci curvature on every four-dimensional simply connected T ²-manifold.