Pseudo-Riemannian manifolds with recurrent spinor fields

The existence of a recurrent spinor field on a pseudo-Riemannian spin manifold $(M,g)$ is closely related to the existence of a parallel 1-dimensional complex subbundle of the spinor bundle of $(M,g)$. We characterize the following simply connected pseudo-Riemannian manifolds admitting such subbundles in terms of their holonomy algebras: Riemannian manifolds; Lorentzian manifolds; pseudo-Riemannian manifolds with irreducible holonomy algebras; pseudo-Riemannian manifolds of neutral signature admitting two complementary parallel isotropic distributions.Comment: 13 pages, the final versio

On the local structure of Lorentzian Einstein manifolds with parallel distribution of null lines

We study transformations of coordinates on a Lorentzian Einstein manifold with a parallel distribution of null lines and show that the general Walker coordinates can be simplified. In these coordinates, the full Lorentzian Einstein equation is reduced to equations on a family of Einstein Riemannian metrics.Comment: Dedicated to Dmitri Vladimirovich Alekseevsky on his 70th birthda

The efficiency of combined electrothermal and electrochemical accumulation of electricity of a photovoltaic power plant

The relevance of the research is caused by the fact that renewable energy, in particular, photovoltaic generation is becoming essential support in the decentralized systems in Russia. However, the high cost of the power equipment of photovoltaic power plants is a deterrent to their wide practical application. This paper presents the method for reducing the cost of photovoltaic power plants by optimizing energy conversion processes in isolated power supply systems. The characteristics of equipment for photovoltaic generation and the subsequent conversion of parameters and power storage is an urgent task are presented

How to find the holonomy algebra of a Lorentzian manifold

Manifolds with exceptional holonomy play an important role in string theory, supergravity and M-theory. It is explained how one can find the holonomy algebra of an arbitrary Riemannian or Lorentzian manifold. Using the de~Rham and Wu decompositions, this problem is reduced to the case of locally indecomposable manifolds. In the case of locally indecomposable Riemannian manifolds, it is known that the holonomy algebra can be found from the analysis of special geometric structures on the manifold. If the holonomy algebra $\mathfrak{g}\subset\mathfrak{so}(1,n-1)$ of a locally indecomposable Lorentzian manifold $(M,g)$ of dimension $n$ is different from $\mathfrak{so}(1,n-1)$, then it is contained in the similitude algebra $\mathfrak{sim}(n-2)$. There are 4 types of such holonomy algebras. Criterion how to find the type of $\mathfrak{g}$ are given, and special geometric structures corresponding to each type are described. To each $\mathfrak{g}$ there is a canonically associated subalgebra $\mathfrak{h}\subset\mathfrak{so}(n-2)$. An algorithm how to find $\mathfrak{h}$ is provided.Comment: 15 pages; the final versio

One component of the curvature tensor of a Lorentzian manifold

The holonomy algebra \g of an $n+2$-dimensional Lorentzian manifold $(M,g)$ admitting a parallel distribution of isotropic lines is contained in the subalgebra \simil(n)=(\Real\oplus\so(n))\zr\Real^n\subset\so(1,n+1). An important invariant of \g is its \so(n)-projection \h\subset\so(n), which is a Riemannian holonomy algebra. One component of the curvature tensor of the manifold belongs to the space \P(\h) consisting of linear maps from \Real^n to \h satisfying an identity similar to the Bianchi one. In the present paper the spaces \P(\h) are computed for each possible \h. This gives the complete description of the values of the curvature tensor of the manifold $(M,g)$. These results can be applied e.g. to the holonomy classification of the Einstein Lorentzian manifolds.Comment: An extended version of a part from arXiv:0906.132