On 2-quasi-umbilical pseudosymmetric hypersurfaces in the Euclidean space.
Using the fundamental notions of the quaternionic analysis we show that there are no 4-dimensional almost Kähler manifolds which are locally conformally flat with a metric of a special form.
Almost hermitian manifolds, whose Riemann curvature tensor satisfies an almost complex Bianchi-type identity, are considered. Some local and global theorems are proved. The special cases of parakähler manifolds and of Kähler manifolds are examined.
This note gives a generalization of spherical twists, and describe the autoequivalences associated to certain non-spherical objects. Typically these are obtained by deforming the structure sheaves of -curves on threefolds, or deforming -objects introduced by D.Huybrechts and R.Thomas.