Quasitoric Totally Normally Split Representatives in the Unitary Cobordism Ring

A smooth stably complex manifold is said to be totally tangentially/normally split if its stably tangential/normal bundle is isomorphic to a sum of complex line bundles. It is proved that each class of degree greater than 2 in the graded unitary cobordism ring contains a quasitoric totally tangentially and normally split manifold.

     

Classification Problem for Quasitoric Manifolds over a Given Simple Polytope

The classification problem for quasitoric manifolds over a given polytope Pⁿ is considered. The known construction of weights, which was used in the study of the similar problem for toric manifolds, is modified. The construction thus obtained is applied to the solution of the above problem in small dimensions. Classification results are also obtained for polytopes that are products of finitely many simplices of arbitrary dimensions.     

某些黎曼流形中的全脐子流形

The main result obtaind in this paper is that :Let M be a totally umbilical submanifolds in Riemannian manifold N. If the Weyl conformal curvature tensor for N satisfies the following condition: ▽_xC=ω(X)C, for some 1-form ω and any vector field X in M, then M is con-formally flat or it is totally geodesic .     

关于容许全脐超曲面正交族的Einstein流形

The aim of the present paper is to study globally the Riemannian manifold admitting two or more mutually orthogonal families of totally umbilical hypersurfaccs of which each is Einsteinian. This paper consists of four parts: (i) to establish anew the canonical form of the metric of (M,g) admitting p (p≥2) families of mutually orthogonal totally umbilical hypcrsurf aces from the standpoint of global differential geometry; (ii) to prove in a n-dimensional (n>2) Einsteinian manifold E_n of nonvanishing scalar curvature there doesn't exist one family of compact totally geodesic Einsteinian hypersurfaces (Theorem 1);(iii) to prove in a n-dimensional (n≥5) Einsteinian manifold E_n of nonnegative scalar curvature R there don't exist two orthogonal families of totally umbilical but not geodesic complete Einsteinian hypersurfaces (Theorem Ⅱ);(iv) to show that a n-dimensional (n≥5) Riemannian manifold of negative constant scalar curvature R.     

The Totally Geodesic Coisotropic Submanifolds in Kähler Manifolds

In this paper, we consider the coisotropic submanifolds in a Kähler manifold of nonnegative holomorphic curvature. We prove an intersection theorem for compact totally geodesic coisotropic submanifolds and discuss some topological obstructions for the existence of such submanifolds. Our results apply to Lagrangian submanifolds and real hypersurfaces since the class of coisotropic submanifolds includes them. As an application, we give a fixed-point theorem for compact Kähler manifolds with positive holomorphic curvature. Also, our results can be further extended to nearly Kähler manifolds.     

Normally presented varieties

Presented by W. Taylor.     

Normally Ordered Inverse Semigroups

NO of all normally ordered inverse semigroups. We show that the pseudovariety of inverse semigroups PCS generated by all semigroups of injective and order partial transformations on a finite chain consists of all aperiodic elements of NO . Also, we prove that NO is the join pseudovariety of inverse semigroups. PCS V G , where G is the pseudovariety of all finite groups.     

Trans-Sasakian Manifolds Homothetic to Sasakian Manifolds

Mediterranean Journal of Mathematics - In this paper, it is shown that for a 3-dimensional compact simply connected trans-Sasakian manifold of type $${(alpha,beta)}$$ , the smooth functions...     

Normally contracting Lie group actions

We show that there are no normally contracting actions of unimodular Lie groups on closed manifolds.     

Normally Preordered Spaces and Utilities

In applications it is useful to know whether a topological preordered space is normally preordered. It is proved that every k _ω -space equipped with a closed preorder is a normally preordered space. Furthermore, it is proved that second countable regularly preordered spaces are perfectly normally preordered and admit a countable utility representation.     

Graphlike Manifolds

ＧｒａｐｈｌｉｋｅＭａｎｉｆｏｌｄｓ￥ＬｉｕＹａｘｉｎｇ；ＬｉＱｉｓｈｅｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｅｎａｎＵｎｉｖｅｒｓｉｔｙ，Ｋａｉｆｅｎｇ４７５００１，ＰＲＣ）Ａｂｓｔｒａｃｔ：Ｔｈｅｄｉｓｃｏｖｅｒｙｏｆｍａｎｉｆ...     

Totally smooth renormings

Archiv der Mathematik - We study the problem of totally smooth renormings of Banach spaces and provide such renormings for spaces which are weakly compactly generated. We also consider renormings...     

Totally Splittable Polytopes

A split of a polytope is a (necessarily regular) subdivision with exactly two maximal cells. A polytope is totally splittable if each triangulation (without additional vertices) is a common refinement of splits. This paper establishes a complete classification of the totally splittable polytopes.     

完全超紧图

Chia G.L.和Lim C.K.在东南亚第一次图论会议(1983,新加坡)文集的末尾提出六个未解决问题.第五个问题是:设H是自补图,问是否存在自补完全超紧图G,使G~*=H.第六个问题是:设G是完全超紧图.如果G_0与(?)同构,问G是否自补图.本文肯定地回答了第五个问题和否定地回答了第六个问题.     

Totally positive matrices

Though total positivity appears in various branches of mathematics, it is rather unfamiliar even to linear algebraists, when compared with positivity. With some unified methods we present a concise survey on totally positive matrices and related topics.