A scalar valued set function on a Cartesian product of σ-algebras is a Fréchet measure if it is a scalar measure independently in each coordinate. A basic question is considered: is it possible to construct products of Fréchet measures that are analogous to product measures in the classical theory? A Fréchet measure is said to be projectively bounded if it satisfies a Grothendieck type inequali...

In this study we introduce a new tensor in semi-Riemannian manifold, named the M*-projective curvature which generalizes m-projective tensor. We start by deducing some fundamental geometric properties of After that, pseudo symmetric manifolds (PM?S)n. A non-trivial example has been used to show existence such manifold. series interesting conclusions. establish, among other things, that if scala...

Locally flat Finsler metrics arise from information geometry. Some speciel locally dually flat Finsler metrics had been studied in Cheng et al. [3] and Xia [4] respectively. As we konw, a new class of Finsler metrics called general (α, β)-metrics are introduced, which are defined by a Riemannian metrics α and 1-form β. These metrics generalize (α, β)-metrics naturally. In this paper, we give a ...

In this paper all coordinates in two variables over a Noetherian Q-domain of Krull dimension one are proved to be projectively tame. In order to do this, some results concerning projectively-tameness of polynomials in general are shown. Furthermore, we deduce that all automorphisms in two variables over a Noetherian reduced ring of dimension zero are tame.

We show that there exist non-trivial PL knots S n−2 ⊂ S n , n ≥ 5, whose complements have the homotopy type of circles. This is in contrast to the case of smooth, PL locally-flat, and topological locally-flat knots, for which it is known that if the complement has the homotopy type of a circle, then the knot is trivial. It is well-known that if the complement of a smooth, PL locally-flat, or to...

We study a fully nonlinear flow for conformal metrics. The long-time existence and the sequential convergence of flow are established for locally conformally flat manifolds. As an application, we solve the σk-Yamabe problem for locally conformal flat manifolds when k 6= n/2.

In this note we study the conformal metrics of constant Q curvature on closed locally conformally flat manifolds. We prove that for a closed locally conformally flat manifold of dimension n ≥ 5 and with Poincarë exponent less than n−4 2 , the set of conformal metrics of positive constant Q and positive scalar curvature is compact in the C∞ topology.