We prove that continuous groups of isometries at a compact boundary (∂M, γ) extend to continuous groups of isometries of any Einstein filling manifold (M, g) provided, for instance, π1(M,∂M) = 0.

In this paper, we have studied warped products and multiply warped product on quasi-Einstein manifold with semi-symmetric nonmetric connection. Then we have applied our results to generalized Robertson-Walker space times with a semi-symmetric non-metric connection.

A Riemannian manifold (M, g) is semi-symmetric if (R(X,Y ) ◦ R)(U, V,W ) = 0. It is called pseudo-symmetric if R ◦ R = F, F being a given function of X, . . . ,W and g. It is called partially pseudosymmetric if this last relation is fulfilled by not all values of X, . . . ,W . Such manifolds were investigated by several mathematicians: I.Z. Szabó, S. Tanno, K. Nomizu, R. Deszcz and others. In t...

Let (M,ω, J) be a compact and connected polarized Hodge manifold, S an isodrastic leaf of half-weighted Bohr-Sommerfeld Lagrangian submanifolds. We study the relation between the Weinstein symplectic structure of S and the asymptotics of the the pull-back of the Fubini-Study form under the projectivization of the so-called BPU maps on S.

We find a new family of AdS4 vacua in IIA string theory. The internal space is topologically either the complex projective space CP or the “flag manifold” SU(3)/(U(1)×U(1)), but the metric is in general neither Einstein nor Kähler. All known moduli are stabilized by fluxes, without using quantum effects or orientifold planes. The analysis is completely ten–dimensional and does not rely on assum...

The global holomorphic invariant αG(X) introduced by Tian [?], Tian and Yau [?] is closely related to the existence of Kähler-Einstein metrics. In his solution to the Calabi conjecture, Yau [?] proved the existence of a Kähler-Einstein metric on compact Kähler manifolds with nonpositive first Chern class. Kähler-Einstein metrics do not always exist in the case when the first Chern class is posi...

N. Hitchin [H] proved that the Euler characteristic χ(E) and signature σ(E) of a compact orientable 4-dimensional Einstein manifold E satisfy the inequality |σ(E)| 6 2 3χ(E), the equality holding only if either E is flat or the universal covering X of E is a K3-surface and π1(E) = 1, Z/2, or Z/2× Z/2. In the latter cases, E is a K3-surface if π1 = 1, an Enriques surface if π1 = Z/2, or the quot...

We prove that a minimal isometric immersion of a Kähler-Einstein or homogeneous Kähler manifold into an Euclidean space must be totally geodesic. As an application we show that an open subset of the real hyperbolic plane RH2 cannot be minimally immersed into the Euclidean space. As another application we prove that if an irreducible Kähler manifold is minimally immersed in an Euclidean space th...

This paper aims to classify the holonomy of the conformal Tractor connection, and relate these holonomies to the geometry of the underlying manifold. The conformally Einstein case is dealt with through the construction of metric cones, whose Riemannian holonomy is the same as the Tractor holonomy of the underlying manifold. Direct calculations in the Ricci-flat case and an important decompositi...