We study the local Killing Lie algebra of meromorphic almost rigid geometric structures on complex manifolds. This leads to classification results for compact complex manifolds bearing holomorphic rigid geometric structures.

We study generalized Kähler manifolds for which the corresponding complex structures commute and classify completely the compact generalized Kähler four-manifolds for which the induced complex structures yield opposite orientations.

Assume (M,ω) is a connected, compact 6 dimensional symplectic manifold equipped with a semi-free Hamiltonian circle action, such that the fixed point set consists of isolated points or compact orientable surfaces. We restrict attention to the case dim H(M) < 3. We give a complete list of the possible manifolds, determine their equivariant cohomology ring and equivariant Chern classes. Some of t...

We construct examples of compact hyperkähler manifolds with torsion (HKT manifolds) which are not homogeneous and not locally conformal hyperkähler. Consider a total space T of a tangent bundle over a hyperkähler manifold M . The manifold T is hypercomplex, but it is never hyperkähler, unless M is flat. We show that T admits an HKT-structure. We also prove that a quotient of T by a Z-action v −...

We study codimension one holomorphic foliations on complex projective spaces and compact manifolds under the assumption that the foliation has a projective transverse structure in the complement of some invariant codimension one analytic subset. The basic motivation is the characterization of pull-backs of Riccati foliations on projective spaces. Our techniques apply to give a description of th...

Among the eigenvalue problems of the Laplacian, the biharmonic operator eigenvalue problems are interesting projects because these problems root in physics and geometric analysis. The buckling problem is one of the most important problems in physics, and many studies have been done by the researchers about the solution and the estimate of its eigenvalue. In this paper, first, we obtain the evol...

We prove that the only complex parabolic geometries on Calabi–Yau manifolds are the homogeneous geometries on complex tori. We also classify the complex parabolic geometries on homogeneous compact Kähler manifolds.

In this note, we will show that the fundamental group of any negatively δ-pinched (δ > 14) manifold can’t be the fundamental group of a quasi-compact Kähler manifold. As a consequence of our proof, we also show that any nonuniform lattice in F4(−20) cannot be the fundamental group of a quasi-compact Kähler manifold. The corresponding result for uniform lattices was proved by Carlson and Hernánd...

We give a summary of known results on Matveev's complexity of compact 3-manifolds. The only relevant new outcome is the classification of all closed orientable irreducible 3-manifolds of complexity 10.

In this note we present a characterization of those open n-manifolds (n ≥ 5), whose products with the real line are homeomorphic to interiors of compact (n + 1)-manifolds with boundary.