Regge manifolds are piecewise continuous manifolds constructed from a finite nutnber of basic building blocks. On such manifolds piecewise continuous forms can be defined in a way similar to differential forms on a differentiable manifold. Regge manifolds are used extensively in the construction ofspace-times in numerical general relativity. In this paper a definition ofexterior differentiation...

A Hermitian Einstein-Weyl manifold is a complex manifold admitting a Ricci-flat Kähler covering M̃ , with the deck transform acting on M̃ by homotheties. If compact, it admits a canonical Vaisman metric, due to Gauduchon. We show that a Hermitian Einstein-Weyl structure on a compact complex manifold is determined by its volume form. This result is a conformal analogue of Calabi’s theorem stating ...

The computation of global invariant manifolds has seen renewed interest in recent years. We survey different approaches for computing a global stable or unstable manifold of a vector field, where we concentrate on the case of a two-dimensional manifold. All methods are illustrated with the same example — the two-dimensional stable manifold of the origin in the Lorenz system.

Let (X,ω) be a polarized simply connected Calabi-Yau manifold. That is, X is a simply connected compact Kähler manifold of dimension n with zero first Chern class and ω is a Kähler form of X such that [ω] ∈ H(X,Z). In this paper, we study the local properties of the moduli space M of the polarized Calabi-Yau manifold (X,ω). By definition M is the parameter space of the complex structures over X...

For a complex manifold M denote by Aut(M) the group of holomorphic automorphisms of M . Equipped with the compact-open topology, Aut(M) is a topological group. We are interested in characterizing complex manifolds by their automorphism groups. One manifold that has been enjoying much attention in this respect is the unit ball B ⊂ C for n ≥ 2. Starting with the famous theorems of Wong [W] and Ro...

We prove analogs of Thom’s transversality theorem and Whitney’s theorem on immersions for pseudo-holomorphic discs. We also prove that pseudo-holomorphic discs form a Banach manifold. MSC: 32H02, 53C15.

INTRODUCTION The Cohomological Field Theory was propose by Kontsevich and Manin [5] for description of Gromov-Witten Classes. They prove that Cohomological Field Theory is equivalent to Formal Frobenius manifold. Formal Frobenius manifold is defined by a formal series F , satisfying to associative equations. In points of convergence the series F defines a Frobenius algebras. The set of these po...

To understand the nature of turbulence, we select 2D Euler equation under periodic boundary condition as our primary example to study. 2D Navier-Stokes equation at high Reynolds number is regarded as a singularly perturbed 2D Euler equation. That is, we are interested in studying the zero viscosity limit problem. To begin an infinite dimensional dynamical system study, we consider a simple fixe...

MR0148075 (26 #5584) 57.10 Kervaire, Michel A.; Milnor, John W. Groups of homotopy spheres. I. Annals of Mathematics. Second Series 77 (1963), 504–537. The authors aim to study the set of h-cobordism classes of smooth homotopy n-spheres; they call this set Θn. They remark that for n = 3, 4 the set Θn can also be described as the set of diffeomorphism classes of differentiable structures on S; b...