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The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry
almost-Riemannian geometry conjugate and cut loci
2010/12/6
We study the tangential case in 2-dimensional almost-Riemannian geometry. We analyse the connection with the Martinet case in sub-Rieman-nian geometry. We compute estimations of the exponential map wh...
Analysis of Riemann Zeta Function Zeros using Pochhammer Polynomial Expansions
Riemann Zeta function Riemann Hypothesis Entire functions Real zeros
2010/12/7
The Riemann Zeta function ζ(s) can be expressed in terms of the entire function ξ(s)which has an integral representation characteristic of a general class of entire functions symmetric
around s = &fr...
Conformal geometry of surfaces in the Lagrangian--Grassmannian and second order PDE
Conformal geometry of surfaces Lagrangian--Grassmannian and second order PDE
2010/12/1
Of all real Lagrangian{Grassmannians LG(n; 2n), only LG(2; 4) admits a distinguished Lorentzian) conformal structure and hence is identi ed with the inde nite Mobius space S1;2.
The Isoperimetric Profile of a Noncompact Riemannian Manifold for Small Volumes
Isoperimetric Profile Noncompact Riemannian Manifold for Small Volumes
2010/11/29
Let M be an n-dimensional Riemannian manifold. We deal, mainly, with the problem of finding a relatively compact domain D ⊂⊂ M that minimizes Area(∂D) among domains of the same volum...
Almost commutative Riemannian geometry, I: wave operators
noncommutative geometry quantum groups quantum gravity
2010/12/3
Associated to any (pseudo)-Riemannian manifold M of dimension n is an n + 1-dimensional noncommutative di erential structure (1; d)on the manifold.
Derived Resolution Property for Stacks, Euler Classes and Applications
Derived Resolution Property for Stacks Euler Classes Applications
2010/12/13
By resolving any perfect derived object over a Deligne-Mumford stack, we define its Euler class. We then apply it to define the Euler numbers for a smooth Calabi-Yau threefold in P4. These numbers are...
Exponential convergence to equilibrium for kinetic Fokker-Planck equations on Riemannian manifolds
kinetic Fokker-Planck equations Riemannian manifolds
2010/12/13
A class of linear kinetic Fokker-Planck equations with a non-trivial dif-fusion matrix and with periodic boundary conditions in the spatial vari-able is considered. After formulating the problem in a ...
Sectional Curvature in terms of the Cometric, with Applications to the Riemannian Manifolds of Landmarks
shape spaces landmark points cometric sectional curvature
2010/12/6
This paper deals with the computation of sectional curvature for the manifolds of N land-
marks (or feature points) in D dimensions, endowed with the Riemannian metric induced by the
group action of...
Parahoric bundles on a compact Riemann surface
Stable vector bundles parahoric groups parabolic bundles
2010/12/8
Let Y be a smooth projective curve (defined over the ground field C) with an action of a finite group . Let X be the smooth projective curve Y/ and let p : Y → X be the quotient mo...
The Bergman property for endomorphism monoids of some Fraïssé limits
Bergman property for endomorphism monoids Fraï ssé limits
2010/12/3
Based on an idea of Y. P´eresse and some results ofMaltcev, Mitchell and Ruˇskuc,we present sufficient conditions under which the endomorphism monoid of an ultrahomogeneous first-order structure...
Flat Pseudo-Riemannian Homogeneous Spaces with Non-Abelian Holonomy Group
Flat Pseudo-Riemannian Homogeneous Spaces Non-Abelian Holonomy Group
2010/12/8
We construct homogeneous flat pseudo-Riemannian manifolds with non-abelian fundamental group. In the compact case, all homogeneous flat pseudo-Riemannian manifolds are complete and have abelian linear...
混合投影体的极与混合相交体的Aleksandrov-Fenchel不等式的稳定性
吴大任——我国积分几何研究的先驱之一（图）
中国科学技术专家传略编辑部 积分几何 非欧几何 微分几何
2009/5/13
吴大任，数学家，数学教育家。长期担任南开大学领导工作与教学工作，著、译数学教材及名著多种。对我国高等教育事业作出了积极贡献。研究领域涉及积分几何、非欧几何、微分几何及其应用（齿轮理论）。
本文利用杨路和张景中创造的特征根的方法和Darboux定理,将著名的杨-张不等式推广到$n$维欧氏空间的两个完全同向的有限质点组中,获得了有限质点组的一类几何不等式,作为其应用,给出了一些新的三角形不等式.
不可思议的几何—非欧几何
非欧几何 罗式几何 黎曼几何
2005/8/12
非欧几何学是一门大的数学分支，一般来讲 ，他有广义、狭义、通常意义这三个方面的不同含义。所谓广义式泛指一切和欧几里的几何学不同的几何学，狭义的非欧几何只是指罗式几何来说的，至于通常意义的非欧几何，就是指罗式几何和黎曼几何这两种几何。