We prove a relative version of Kontsevich’s formality theorem. This theorem involves a manifold M and a submanifold C and reduces to Kontsevich’s theorem if C=M. It states that the DGLA of multivector fields on an infinitesimal neighbourhood of C is L∞-quasiisomorphic to the DGLA of multidifferential operators acting on sections of the exterior algebra of the conormal bundle. Applications to th...

The main purpose of the following article is to give a proof of Y. Kawa-mata's celebrated subadjunction theorem in the spirit of our previous work on Bergman kernels. We will use two main ingredients : an L 2 m –extension theorem of Ohsawa-Takegoshi type (which is also a new result) and a more complete version of our former results. §0 Introduction Let X be a projective manifold and let Θ be a ...

The center manifold is an invariant that plays a crucial role in the bifurcation analysis of dynamical systems. existence theorem assures local submanifold state space system around non-hyperbolic equilibrium point. Center theory essential reduction different scenarios to their normal forms. Our study focuses on predator-prey interactive with density-dependent growth predators subject contagiou...

We establish a S1-equivariant index theorem for Dirac operators on Z/kmanifolds. As an application, we generalize the Atiyah-Hirzebruch vanishing theorem for S1-actions on closed spin manifolds to the case of Z/k-manifolds. Résumé français On établit un théorème d’indice S-équivariant pour les opérateurs de Dirac sur des Z/k variétés. On donne une application de ce résultat, qui généralise le t...

In this paper one first shows that the slow flow of a mechanical system with unstable mode coupled to Nonlinear Energy Sink (NES) can be reduced, in neighborhood fold point its critical manifold, normal form dynamic saddle-node bifurcation. This allows us then obtain scaling law for dynamics and improve accuracy theoretical prediction mitigation limit NES previously obtained as part zeroth-orde...

Thurston’s hyperbolic Dehn surgery theorem is one of the most important results in 3-manifold theory, and it has stimulated an enormous amount of research. IfM is a compact orientable hyperbolic 3-manifold with boundary a single torus, then the theorem asserts that, for all but finitely many slopes s on ∂M , the manifold M(s) obtained by Dehn filling along s also admits a hyperbolic structure. ...

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 ...

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...