On asymptotically complex hyperbolic (ACH) Einstein manifolds, we consider a certain variational problem for almost structures compatible with the metric, which linearized Euler-Lagrange equation at K\"ahler-Einstein is given by Dolbeault Laplacian acting on $(0,1)$-forms values in holomorphic tangent bundle. A deformation result of ACH metrics associated critical this given. It also shown that...

We study the space of (orthogonal) almost complex structures on closed six-dimensional manifolds as sections twistor for a given metric. For connected six-manifold with vanishing first Betti number, we express quotient seven-sphere bundle over manifold by circle action, and then use this description to compute rational homotopy theoretic minimal model components that satisfy certain Chern numbe...

We study balanced Hermitian structures on almost abelian Lie algebras, i.e. algebras with a codimension-one ideal. In particular, we classify six-dimensional which carry structure. It has been conjectured in [1] that compact complex manifold admitting both metric and an SKT necessarily Kähler metric: prove this conjecture for solvmanifolds left-invariant structures. Moreover, investigate the be...