Related papers: Projective differential geometry and asymptotic an…

A symplectic structure on the space of nondegenerate and nonparametrized curves in a locally affine manifold is defined. We also consider several interesting spaces of nondegenerate projective curves endowed with Poisson structures. This…

We generalize double bracket vector fields, originally defined on semisimple Lie algebras, to Poisson manifolds equipped with a pseudo-Riemannian metric by utilizing a symmetric contravariant 2-tensor field. We extend the normal metric on…

In the article we discuss the notion of the generalized invariant manifold introduced in our previous study. In the literature the method of the differential constraints is well known as a tool for constructing particular solutions for the…

We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…

The aim of this paper is to give a new description of the geometry appearing in the multi-specialization along a general family of submanifolds of a real analytic manifold (including some important cases as clean intersection or a…

In this work, we study the asymptotic geometry of the mapping class group and Teichmueller space. We introduce tools for analyzing the geometry of `projection' maps from these spaces to curve complexes of subsurfaces; from this we obtain…

The tools developed in a preceding article for interpreting spacetime geometry in terms of all possible space-plus-time splitting approaches are applied to circular orbits in some familiar stationary axisymmetric spacetimes. This helps give…

In this note, we compute the group of automorphisms of Projective, Affine and Euclidean Geometries in the sense of Klein. As an application, we give a simple construction of the outer automorphism of S_6.

We construct a family of canonical connections and surrounding basic theory for almost complex manifolds that are equipped with an affine connection. This framework provides a uniform approach to treating a range of geometries. In…

We show how the theory of $\mathbb{Z}_2^n$ -manifolds - which are a non-trivial generalisation of supermanifolds - may be useful in a geometrical approach to mixed symmetry tensors such as the dual graviton. The geometric aspects of such…

We study a deformation of infinitesimal diffeomorphisms of a smooth manifold. The deformation is based on a general twist. This leads to a differential geometry on a noncommutative algebra of functions whose product is a star-product. The…

We develop a method for evaluating asymptotics of certain contour integrals that appear in Conformal Field Theory under the name of Dotsenko-Fateev integrals and which are natural generalizations of the classical hypergeometric functions.…

We present a generalisation of the theory of iterated function systems and associated fractals to the setting of noncommutative geometry. Along the way, we discuss some ideas surrounding locally compact noncommutative metric spaces.

The fourth derivative models for two dimensional gravity are shown to be equivalent to the special version of the nonlinear sigma models coupled to 2d quantum gravity. The reduction consists in the introduction of the auxiliary scalar…

Co lombeau's construction of generalized functions (in its special variant) is extended to a theory of generalized sections of vector bundles. As particular cases, generalized tensor analysis and exterior algebra are studied. A point value…

Extremal length is a classical tool in 1-dimensional complex analysis for building conformal invariants. We propose a higher-dimensional generalization for complex manifolds and provide some ideas on how to estimate and calculate it. We…

Starting from the concept of the universal exterior algebra in non-commutative differential geometry we construct differential forms on the quantum phase-space of an arbitrary system. They bear the same natural relationship to quantum…

We study the Dirichlet problem for semilinear equations on general open sets with measure data on the right-hand side and irregular boundary data. For this purpose we develop the classical method of orthogonal projection. We treat in a…

Symplectic and Poisson geometry emerged as a tool to understand the mathematical structure behind classical mechanics. However, due to its huge development over the past century, it has become an independent field of research in…

We develop a geometric framework to address asymptoticity and nonexpansivity in topological dynamics. Our framework can be applied when the acting group is second countable and locally compact. As an application, we show extensions of…