where k is the first Betti number b^M), T is a flat riemannian λ -torus, M~ is a compact connected Ricci-flat (n — λ;)-manifold, and Ψ is a finite group of fixed point free isometries of T x M' of a certain sort (Theorem 4.1). This extends Calabi's result on the structure of compact euclidean space forms ([7] see [20, p. 125]) from flat manifolds to Ricci-flat manifolds. We use it to essentiall...

We show that any non-Kähler, almost Kähler 4-manifold for which both the Ricci and the Weyl curvatures have the same algebraic symmetries as they have for a Kähler metric is locally isometric to the (only) proper 3-symmetric four-dimensional space. Mathematics Subject Classifications (2000): Primary 53B20, 53C25.

We build blowing-up solutions for a supercritical perturbation of the Yamabe problem on manifolds with umbilic boundary, provided dimension manifold is n ≥ 8 and that Weyl tensor W g not vanishing ∂ M .

Under intrinsic and extrinsic curvature assumptions on a Riemannian spin manifold and its boundary, we show that there is an isomorphism between the restriction to the boundary of parallel spinors and extrinsic Killing spinors of nonnegative Killing constant. As a corollary, we prove that a complete Ricci-flat spin manifold with mean-convex boundary isometric to a round sphere, is necessarily a...

In this paper, we apply the theory of Chern-Cheeger-Simons to construct canonical invariants associated to an r-simplex whose points parametrize flat connections on a smooth manifold X. These invariants lie in degrees (2p − r − 1)-cohomology with C/Z-coefficients, for p > r ≥ 1. This corresponds to a homomorphism on the higher homology groups of the moduli space of flat connections, and taking ...

Let X be a compact Kähler manifold with zero first Chern class, and let L be an ample line bundle overX . The pair (X,L) is called a polarized Calabi-Yaumanifold. By Yau’s proof of the Calabi conjecture, we know such a manifold carries a unique Ricci flat metric compatable with the polarization (cf. [37]). Thus, the moduli space of such Ricci flat Kähler metrics is the moduli space of complex s...

The assumption in the main result of [2] is removed Let G be a Lie group which acts isometrically on a Riemannian manifold M . A section of the Riemannian G-manifold M is a closed submanifold Σ which meets each orbit orthogonally. In this situation the trace on Σ of the G-action is a discrete group action by the generalized Weyl group W (Σ) = NG(Σ)/ZG(Σ), where NG(Σ) := {g ∈ G : g.Σ = Σ} and ZG...

We construct a Kähler structure (which we call a generalised Kähler cone) on an open subset of the cone of a strongly pseudo-convex CR manifold endowed with a 1-parameter family of compatible Sasaki structures. We determine those generalised Kähler cones which are Bochner-flat and we study their local geometry. We prove that any Bochner-flat Kähler manifold of complex dimension bigger than two ...

In this article, the aim is to introduce a para-Sasakian manifold with a canonical paracontact connection. It is shown that φ−conharmonically flat , φ−W2 flat and φ−pseudo projectively flat para-Sasakian manifolds with respect to canonical paracontact connection are all η−Einstein manifolds. Also, we prove that quasi-pseudo projectively flat para-Sasakian manifolds are of constant scalar curvat...

We introduce a symplectic structure on the space of connections in a G-principal bundle over a four-manifold and the Hamiltonian action on it of the group of gauge transformations which are trivial on the boundary. The symplectic reduction becomes the moduli space of flat connections over the manifold. On the moduli space of flat connections we shall construct a hermitian line bundle with conne...