An analogy of Tian-Todorov theorem on deformations of CR-structures
In [11] we have considered a family of almost anti-Hermitian structures (G,J) on the tangent bundle TM of a Riemannian manifold (M,g), where the almost complex structure J is a natural lift of g to TM interchanging the vertical and horizontal distributions VTM and HTM and the metric G is a natural lift of g of Sasaki type, with the property of being anti-Hermitian with respect to J. Next, we have studied the conditions under which (TM,G,J) belongs to one of the eight classes of anti-Hermitian structures...
Donaldson proved that if a polarized manifold has constant scalar curvature Kähler metrics in and its automorphism group is discrete, is asymptotically Chow stable. In this paper, we shall show an example which implies that the above result does not hold in the case where is not discrete.
We show that there exist astheno-Kähler structures on Calabi-Eckmann manifolds.