相关论文: Dilatation structures in sub-riemannian geometry

One of effective ways to solve the equivalence problem and describe moduli spaces for real submanifolds in complex space is the normal form approach. In this survey, we outline some normal form constructions in CR-geometry and formulate a…

In this paper we continue the study of dilatation structures, introduced in math.MG/0608536 . A dilatation structure on a metric space is a kind of enhanced self-similarity. By way of examples this is explained here with the help of the…

The twistor construction for Riemannian manifolds is extended to the case of manifolds endowed with generalized metrics (in the sense of generalized geometry \`a la Hitchin). The generalized twistor space associated to such a manifold is…

Submanifold theory is a very active vast research field which plays an important role in the development of modern differential geometry. This branch of differential geometry is still so far from being exhausted; only a small portion of an…

It is well-known that the class of piecewise smooth curves together with a smooth Riemannian metric induces a metric space structure on a manifold. However, little is known about the minimal regularity needed to analyze curves and…

Generalized complex geometry, as developed by Hitchin, contains complex and symplectic geometry as its extremal special cases. In this thesis, we explore novel phenomena exhibited by this geometry, such as the natural action of a B-field.…

Motivated by a paper of Zirnbauer, we develop a theory of Riemannian supermanifolds up to a definition of Riemannian symmetric superspaces. Various fundamental concepts needed for the study of these spaces both from the Riemannian and the…

This paper is the third in a series dedicated to the fundamentals of sub-Riemannian geometry and its implications in Lie groups theory: "Sub-Riemannian geometry and Lie groups. Part I", math.MG/0210189, available at…

This paper develops a deformation-field geometry for spaces whose local frames may undergo internal stretching, compression, and shear. Ordinary Riemannian geometry takes an intrinsic metric geometry \((M,g)\) as the given datum and uses…

A generalization of the notion of a (pseudo-) Riemannian space is proposed in a framework of noncommutative geometry. In particular, there are parametrized families of generalized Riemannian spaces which are deformations of classical…

In the last two decades, one of the most important developments in Riemannian geometry is the collapsing theory of Cheeger-Fukaya-Gromov. A Riemannian manifold is called (sufficiently) collapsed if its dimension looks smaller than its…

In this paper we give a generalization of the normal holomorphic frames in the symplectic manifolds and find conditions for the integrability of complex structures.

On the Grassmann manifold G (m, n) of m-dimensional subspaces of an n-dimensional projective space P^n, a certain supplementary construction called the normalization is considered. By means of this normalization, one can construct the…

In this article we show how holomorphic Riemannian geometry can be used to relate certain submanifolds in one pseudo-Riemannian space to submanifolds with corresponding geometric properties in other spaces. In order to do so, we shall first…

A dilatation structure on a metric space, arXiv:math/0608536v4, is a notion in between a group and a differential structure, accounting for the approximate self-similarity of the metric space. The basic objects of a dilatation structure are…

In this paper I explain what is a pair of dilatation structures, one looking down to another. Such a pair of dilatation structures leads to the intrinsic definition of a distribution as a field of topological filters. To any pair of…

We investigate the geometric and topological structure of equidistant decompositions of Riemannian manifolds.

We study the regularity and branching of strictly abnormal minimizing geodesics in sub-Riemannian geometry. We construct examples of real-analytic sub-Riemannian manifolds admitting minimizing geodesics that lose regularity at an interior…

Concepts and techniques from the theory of G-structures of higher order are applied to the study of certain structures (volume forms, conformal structures, linear connections and projective structures) defined on a pseudo-Riemanniann…

We discuss regularity statements for equidistant decompositions of Riemannian manifolds and for the corresponding quotient spaces. We show that any stratum of the quotient space has curvature locally bounded from both sides.