1,721,033 research outputs found
ON THE CURVATURES OF EINSTEIN-SPACES
No full textFor a pseudo-Riemannian manifold (M,g) of dimension n greater than or equal to 3, we introduce a scalar curvature function S(V) for non-degenerate subspaces V of T(p)M which is a generalization of the scalar curvature, and give some characterizations of Einstein spaces in terms of this scalar curvature function. We also give a characterization for spaces of constant curvature. As an application of our results, we show that the Ricci curvature or the sectional curvature of a Lorentz manifold is constant if the scalar curvature function for non-degenerate subspaces is bounded.X11sciescopu
Geometric inequalities for spacelike hypersurfaces in the Minkowski spacetime
No full textWe derive a linear isoperimetric inequality and some geometric inequalities for properly located compact achronal spacelike hypersurfaces via a Minkowski-type integral formula in the Minkowski spacetime. (C) 2001 Elsevier Science B.V. All rights reserved. MSC: 53C50; 52A40.X111sciescopu
ON SOME SPECIAL CLASSES OF KENMOTSU MANIFOLDS
No full textWe investigate the classes of Kenmotsu manifolds which satisfy the condition of being eta-Einstein, having eta-parallel Ricci tensor, R(xi, X) (.) Z = 0, R(xi, X) (.) R = 0, Z(xi, X) (.) Z = 0, Z(xi, X) (.) R = 0, Z(xi, X) (.) S = 0 or being Ricci-pseudosymmetric, where R, Z and S denote the curvature tensor, the concircular curvature tensor and the Ricci tensor, respectively. We also prove that a transformation in a Kenmotsu manifold under certain conditions is an isometry.X117sciescopu
Enhancing the tracking performance in optical storage systems using a disturbance compensator
No full text
Regular graph coverings whose covering transformation groups have the isomorphism extension property
No full textEnumerative results are presently a major center of interest in topological graph theory, as in the work of Gross and Furst [1], Hofmeister [5,6], Kwak and Lee [9-13] and Mull et al. [15], etc. Kwak and Lee [9] enumerated the isomorphism classes of graph bundles and those of n-fold graph coverings with respect to a group of automorphisms of the base graph which fix a spanning tree. Hofmeister [6] enumerated independently the isomorphism classes of n-fold graph coverings with respect to the trivial automorphism group of the base graph. But the enumeration of isomorphism classes of regular graph coverings has not been answered completely. As its partial answers, Hofmeister [5] enumerated the isomorphism classes of Z(2)-coverings (double coverings) with respect to any group of automorphisms of the base graph, and Sate [14] did the same work for Z(p)-coverings (regular prime-fold coverings). With respect to the trivial automorphism group of the base graph, Hong and Kwak [8] did the same work for Z(2) + Z(2) or Z(4)-coverings, and Kwak and Lee [10] did it for Z(p), Z(p) + Z(q) (p not equal q primes) or Z(p2)-coverings. As an expansion of this effort, we obtain in this paper several new algebraic characterizations for isomorphic regular coverings and derive an enumerating formula for the isomorphism classes of A-coverings of a graph G with respect to any group of automorphisms of G which fix a spanning tree, when the covering transformation group A has the isomorphism extension property. By definition, it means that every isomorphism between any two isomorphic subgroups B-1 and B-2 of A can be extended to an automorphism of A. Also, we obtain complete numerical enumeration of the isomorphism classes of Z(n)-coverings for all n, D-n-coverings for odd n (D-n is the dihedral group of order 2n) or Z(p) + Z(n)-coverings of a graph G for prime p with respect to the trivial automorphism group of G. In addition, we applied our results to a bouquet of circles.X1125sciescopu
Bipartite graph bundles with connected fibres
No full textLet G be a finite connected simple graph. The isomorphism classes of graph bundles and graph coverings over G have been enumerated by Kwak and Lee. Recently, Archdeacon and others characterised bipartite coverings of G and enumerated the isomorphism classes of regular 2p-fold bipartite coverings of G, when G is nonbipartite: In this paper, we characterise bipartite graph bundles over G and derive some enumeration formulas of the isomorphism classes of them when the fibre is a connected bipartite graph. As an application, we compute the exact numbers of the isomorphism classes of bipartite graph bundles over G when the fibre is the path P-n or the cycle C-n.X113sciescopu
Isoperimetric numbers and bisection widths of double coverings of a complete graph
No full textThe aim of this paper is to study the isoperimetric numbers of double coverings of a complete graph. It turns out that these numbers are very closely related to the bisection widths of the double coverings and the degrees of unbalance of the signed graphs which derive the double coverings. For example, the bisection width of a double covering of a complete graph K-m is equal to m times its isoperimetric number. We determine which numbers can be the isoperimetric numbers of double coverings of a complete graph.X111sciescopu
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