For every n, we construct a metric measure space that is doubling, satisfies a Poincare inequality in the sense of HeinonenKoskela, has topological dimension n, and has a measurable tangent bundle of dimension 1.

We prove that the space of Hamiltonian deformations of zero section in a cotangent bundle of a compact manifold is locally flat in the Hofer metric and we describe its geodesics.

In this paper, we firstly determine a new deformed Sasaki type lift of metric from Riemannian manifold to its coframe bundle and investigate few special (1.1)-tensor structures (i.e. almost Hermit structures) in the equipped with lift.

the general relatively isotropic mean landsberg metrics contain the general relativelyisotropic landsberg metrics. a class of finsler metrics is given, in which the mentioned two conceptsare equivalent. in this paper, an interpretation of general relatively isotropic mean landsberg metrics isfound by using c-conformal transformations. some necessary conditions for a general relativelyisotropic ...

A stochastic flow is constructed on a frame bundle adapted to a Riemannian foliation on a compact manifold. The generator A of the resulting transition semigroup is shown to preserve the basic functions and forms, and there is an essentially unique strictly positive smooth function φ satisfying Aφ = 0. This function is used to perturb the metric, and an application of the ergodic theorem shows ...

The paper presents an extension of the geometric quantization procedure to integrable, big-isotropic structures. We obtain a generalization of the cohomology integrality condition, we discuss geometric structures on the total space of the corresponding principal circle bundle and we extend the notion of a polarization. 1 Big-isotropic structures Weak-Hamiltonian functions belong to the framewor...

In this paper, we study the class of of C3-like Finsler metrics which contains the class of semi-C-reducible Finsler metric. We find a condition on C3-like metrics under which the notions of Landsberg curvature and mean Landsberg curvature are equivalent.

Let M be a compact complex manifold of complex dimension two with a smooth Kahler metric and D a smooth divisor on M. If E is a rank 2 holomorphic vector bundle on M with a stable parabolic structure along D, we prove that there exists a Hermitian-Einstein metric on E' = E|M\D compatible with the parabolic structure, and whose curvature is square integrable. MIRAMARE TRIESTE January 2000

Abstract We prove the Kobayashi—Hitchin correspondence and approximate for twisted holomorphic vector bundles on compact Kähler manifolds. More precisely, if X is a manifold g Gauduchon metric X, bundle −polystable only it −Hermite-Einstein, , then −semistable −Hermite-Einstein.