Seven Classes of Harmonic Diffeomorphisms

We deduce two necessary and sufficient conditions for a diffeomorphism $f : M \to \overline{M}$ of a Riemannian manifold (M,g) onto a Riemannian manifold $(\overline{M},\bar g)$ to be harmonic. Using the representation theory of groups, we define in an intrinsic way seven classes of such harmonic diffeomorphisms and partly describe the geometry of each class.     

New characteristics of infinitesimal isometry and Ricci solitons

We prove that a vector field X on a compact Riemannian manifold (M, g) with Levi-Cività connection ? is an infinitesimal isometry if and only if it satisfies the system of differential equations: trace _g (L _X ?) = 0, trace _g (L _X Ric) = 0, where L _X is the Lie derivative in the direction of X and Ric is the Ricci tensor. It follows from the second assertion that the Ricci soliton on a compact manifold M is trivial if its vector field X satisfies one of the following two conditions: trace _g (L _X Ric) ≤ 0 or trace _g (L _X Ric) ≥ 0.     

Geometry of Infinitesimal Harmonic Transformations

One of the present authors defined the infinitesimal harmonictransformation in a Riemannian manifold. This paperis devoted to the study of the local and global geometryinfinitesimal harmonic transformations.     

Effect of electron-ion bombardment on the growth of dielectric films in reactive sputtering

The mechanism by which electron — ion bombardment affects the growth of a silicon nitride film obtained by reactive sputtering in an apparatus based on a Penning discharge is investigated. The temperature and the degree of irradiation of the substrate are determined as functions of the distance from the substrate to the aperture in the anode. It is established that the presence or absence of bombardment leads to a difference in the formation of reactively sputtered silicon nitride films.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 11–15, December, 1976.The authors thank Yu. E. Kreindel' for his interest in the work and for useful discussions.