Volume 217, Nº 5 (2016)

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.

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.

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.

In this paper, we examine the problem on the existence of best approximation elements in functional spaces with nonsymmetric norms and sign-sensitive weights.