On a Generalization of Equilogical Spaces

We use the theory of triposes to prove that every (non-degenerate) locale H is the set of truth values of a complete and co-complete quasi-topos into which the category of topological spaces embeds and the topos of sheaves over H reflectively embeds.     

On Formality of a Class of Compact Homogeneous Spaces

We prove the formality property of any homogeneous space G/G generated by an automorphism of finite order of a compact simple Lie group G.     

两点齐性的Finsler流形

该文证明任何一个两点齐性的Finsler流形一定是黎曼流形．证明过程中作者将泛函分析中经典的Mazur定理推广到不一定是绝对齐次的Minkowski空间上．     

两点齐性的 Finsler 流形

该文证明任何一个两点齐性的 Finsler 流形一定是黎曼流形. 证明过程中作者将泛函分析中经典的Mazur 定理推广到不一定是绝对齐次的 Minkowski 空间上.     

On Elliptic Homogeneous Differential Operators in Grand Spaces

We give an application of so-called grand Lebesgue and grand Sobolev spaces, intensively studied during last decades, to partial differential equations. In the case of unbounded domains such spaces are defined using so-called grandizers. Under some natural assumptions on the choice of grandizers, we prove the existence, in some grand Sobolev space, of a solution to the equation Pm(D)u(x) = f(x), x ∈ ℝn, m < n, with the right-hand side in the corresponding grand Lebesgue space, where Pm(D) is an arbitrary elliptic homogeneous in the general case we improve some known facts for the fundamental solution of the operator Pm(D): we construct it in the closed form either in terms of spherical hypersingular integrals or in terms of some averages along plane sections of the unit sphere.     

On the Commutativity of Weakly Commutative Riemannian Homogeneous Spaces

A Riemannian homogeneous space X=G/H is said to be commutative if the algebra of G-invariant differential operators on X is commutative and weakly commutative if the associated Poisson algebra is commutative. Clearly, the commutativity of X implies its weak commutativity. The converse implication is proved in this paper.     

Homogeneous Metrics with Nonnegative Curvature

Given compact Lie groups H⊂G, we study the space of G-invariant metrics on G/H with nonnegative sectional curvature. For an intermediate subgroup K between H and G, we derive conditions under which enlarging the Lie algebra of K maintains nonnegative curvature on G/H. Such an enlarging is possible if (K,H) is a symmetric pair, which yields many new examples of nonnegatively curved homogeneous metrics. We provide other examples of spaces G/H with unexpectedly large families of nonnegatively curved homogeneous metrics.     

Toward a Theory of Spaces of Constant Curvature

We construct some examples of three-dimensional metrics of constant curvature defined by the solutions of nonlinear integrable differential equations and their generalizations and study the properties of Riemann extensions of the metrics of constant curvature. We discuss the connection with the theory of normal Riemannian spaces. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 1, pp. 42–54, January, 2006.     

Finite Homogeneous Metric Spaces

Siberian Mathematical Journal - The authors study the class of finite homogeneous metric spaces and some of its important subclasses that have natural definitions in terms of the metrics and...     

Homogeneous Spaces with Sections

We study homogeneous Riemannian manifolds all of whose geodesics can be mapped by some isometry into a fixed homogeneous, connected, totally geodesic submanifold, called section. We show that these spaces are locally symmetric if the section is two-dimensional and give non-symmetric counterexamples with higher-dimensional sections.Mathematics Subject Classification (2000): 53C35, 53C30, 53C22, 57S15     

三维拟常曲率空间

本文证明了三维拟常曲率空间有一些不同于维数n≥4情形的几何性质。特别，作出了两族非共形平坦的三维拟常曲率空间。在物理上，三维拟常曲率空间是带热流的流体物质相对论无转D型宇宙模型的类空超曲面。     

齐型空间上的Lipschitz函数空间

给出了齐型空间上Lipschitz函数空间的两个新的等价范数，证明了Lipschitz函数满足与BMO函数类似的Joho-Nirenberg型不等式．