(untitled) (Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics, 1996)
Let (M,g,J) be 2n-dimensional almost Hermitian manifold, p be an arbitrary point of M, and X,Y be an arbitrary orthonormal pair of tangent vectors in the tangent space M_p. If the plane E^2(p;X,Y) is antiholomorphic, i.e. E^2 JE^2, then we define the linear symmetric operator α_X,Y:M_p → M_p, where α_X,Y(u)=12[R(u,X,Y)+R(u,Y,X)] In the present paper we consider the problem when the trace or the spectrum of the curvature operator α_X,Y depends on the point p M and not on the choice of X M_p