In the same spirit as done for N=2 and N=4 supersymmetric non-linear σ models in 2 space-time dimensions by Zumino and AlvarezGaumé and Freedman, we analyse the (2,0) and (4,0) heterotic geometry in holomorphic coordinates. We study the properties of the torsion tensor and give the conditions under which (2,0) geometry is conformally equivalent to a (2,2) one. Using additional isometries, we sh...

We shall give an axiomatic construction of Wess-Zumino-Witten actions valued in G = SU(N), N ≥ 3. It is realized as a functor WZ from the category of conformally flat four-dimensional manifolds to the category of line bundles with connection that satisfies, besides the axioms of a topological field theory, the axioms which abstract WessZumino-Witten actions. To each conformally flat four-dimens...

We prove the existence of smooth closed hypersurfaces of prescribed mean curvature homeomorphic to S for small n, n ≤ 6, provided there are barriers. 0. Introduction In a complete (n+1)-dimensional manifold N we want to find closed hypersurfaces M of prescribed mean curvature. To be more precise, let Ω be a connected open subset of N , f ∈ C(Ω̄), then we look for a closed hypersurface M ⊂ Ω such...

We prove that for each closed smooth spin 4-manifold M there exists a closed smooth 4-manifold N such that M#N admits a conformally at Riemannian metric.

The object of the present paper is to study quasi-conformally flat generalized Sasakian-space-forms. Also we study quasi-conformally semisymmetric generalized Sasakian-space-forms. As a consequence of the results, we obtain some important corollaries.

Let (M, g) be a pseudo-Riemannian manifold and Fλ(M) the space of densities of degree λ on M . We study the space D2 λ,μ(M) of second-order differential operators from Fλ(M) to Fμ(M). If (M, g) is conformally flat with signature p− q, then D2 λ,μ(M) is viewed as a module over the group of conformal transformations of M . We prove that, for almost all values of μ− λ, the O(p+1, q+1)-modules D2 λ...

The concept of conformally equivariant quantizations was introduced by Duval, Lecomte and Ovsienko in [8] for manifolds endowed with flat conformal structures. They obtained results of existence and uniqueness (up to normalization) of such a quantization procedure. A natural generalization of this concept is to seek for a quantization procedure, over a manifold M , that depends on a pseudo-Riem...

In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds r...

The classical Sobolev and Escobar inequalities are embedded into the same oneparameter family of sharp trace-Sobolev inequalities on half-spaces. Equality cases are characterized for each inequality in this family by tweaking a well-known mass transportation argument. The case of the Dirichlet energy corresponds to a family of variational problems on conformally flat metrics, whose absolute min...