On subspaces of C-reducible, semi C-reducible, s3-like and s4-like spaces
The paper deals with tensor fields which are semiconjugated with torse-forming vector fields. The existence results for semitorse-forming vector fields and for convergent vector fields are proved.
In [O2] the Cartan-Norden theorem for real affine immersions was proved without the non-degeneracy assumption. A similar reasoning applies to the case of affine Kähler immersions with an anti-complex shape operator, which allows us to weaken the assumptions of the theorem given in [NP]. We need only require the immersion to have a non-vanishing type number everywhere on M.
Let be a harmonic map from surface into complex Grassmann manifold. In this paper, some sufficient conditions for the harmonic sequence generated by to have degenerate -transform or -transform are given.