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A reflexion space is generalization of a symmetric space introduced by O. Loos. We generalize locally symmetric spaces to local reflexion spaces in the similar way. We investigate, when local reflexio...
Local pinching estimates in 3-dim Ricci flow
Local pinching estimates 3-dim Ricci flow Differential Geometry
2012/6/30
We study curvature pinching estimates of Ricci flow on complete 3- dimensional manifolds without bounded curvature assumption. We will derive some general curvature conditions which are preserved on a...
Bifurcation and local rigidity of homogeneous solutions to the Yamabe problem on spheres
homogeneous solutions Yamabe problem spheres Differential Geometry
2011/9/21
Abstract: We study existence and non existence of constant scalar curvature metrics conformal and arbitrarily close to homogeneous metrics on spheres, using variational techniques. This describes all ...
Local Poincare inequalities from stable curvature conditions on metric spaces
Ricci curvature metric measure spaces geodesics Poincare inequality
2011/9/20
Abstract: We prove local Poincar\'e inequalities under various curvature-dimension conditions which are stable under the measured Gromov-Hausdorff convergence. The first class of spaces we consider is...
Local Equivalence Problem for Sub-Riemannian Structures
Sub-Riemannian Structures Differential Geometry
2011/9/15
Abstract: We solve the local equivalence problem for sub-Riemannian structures on (2n + 1)-dimensional manifolds. We show that two sub-Riemannian structures are locally equivalent if and only if? thei...
Generalized Ricci flow I: Local existence and uniqueness
Generalized Ricci flow uniformly parabolic system short-time existence Thurston’s eight geometries
2011/9/13
Abstract: In this paper we investigate a kind of generalized Ricci flow which possesses a gradient form. We study the monotonicity of the given function under the generalized Ricci flow and prove that...
The Local Product Theorem for bihamiltonian structures
The Local Product Theorem bihamiltonian structures Symplectic Geometry Differential Geometry
2011/9/2
Abstract: In this work one proves that, around each point of a dense open set (regular points), a real analytic or holomorphic bihamiltonian structure decomposes into a product of a Kronecker bihamilt...