We investigate the property of the Wu invariant metric on a certain class of psuedoconvex domains. We show that the Wu invariant Hermitian metric, which in general behaves as nicely as the Kobayashi metric under holomorphic mappings, enjoys the complex hyperbolic curvature property in such cases. Namely, the Wu invariant metric is Kähler and has constant negative holomorphic curvature in a neig...

We give a global picture of the Ricci flow on the space of three-dimensional, unimodular, nonabelian metric Lie algebras considered up to isometry and scaling. The Ricci flow is viewed as a two-dimensional dynamical system for the evolution of structure constants of the metric Lie algebra with respect to an evolving orthonormal frame. This system is amenable to direct phase plane analysis, and ...

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The procedure to find gauge invariant variables for two-parameter nonlinear perturbations in general relativity is considered. Up to third order perturbations, it is shown that appropriate combinations of nonlinear metric perturbations and lower order one are transformed as the gauge transformation of linear order metric perturbations. This implies that gauge invariant variables for the higher ...

For an arbitrary infinite additive group G and for an uncountable compact Hausdorff topological group H with card(H) = card(Hא0) = card(H), H-valued measurable Gprocesses are constructed on the group H and some set-theoretical characteristics of their various F∗(HG)-invariant extensions are calculated, where F∗(HG) denotes a group of transformations of H generated by the eventually neutral sequ...

Let (N, J) be a simply connected 2n-dimensional nilpotent Lie group endowed with an invariant complex structure. We define a left invariant Riemannian metric on N compatible with J to be minimal, if it minimizes the norm of the invariant part of the Ricci tensor among all compatible metrics with the same scalar curvature. In [7], J. Lauret proved that minimal metrics (if any) are unique up to i...

We consider an invariant skew-symmetric phase-space metric for nonHamiltonian systems. We say that the metric is an invariant if the metric tensor field is an integral of motion. We derive the time-dependent skewsymmetric phase-space metric that satisfies the Jacobi identity. The example of non-Hamiltonian systems with linear friction term is considered. PACS numbers: 45.20.−d, 02.40.Yy, 05.20.−y

Let G G be a connected, simply-connected, compact simple Lie group. In this paper, we show that the isometry group of with left-invaria...

Let $K$ be a locally compact hypergroup with left Haar measure and let $L^1(K)$ be the complex Lebesgue space associated with it. Let $L^infty(K)$ be the dual of $L^1(K)$. The purpose of this paper is to present some necessary and sufficient conditions for $L^infty(K)^*$ to have a topologically left invariant mean. Some characterizations of amenable hypergroups are given.