Relative Gottlieb Groups of Embeddings between Complex Grassmannians

Let Gr k , n be the complex Grassmann manifold of k -linear subspaces in ℂ n . We compute rational relative Gottlieb groups of the embedding i : Gr k , n ⟶ Gr k , n + r and show that the G -sequence is exact if r ≥ k n − k .

Rigidity theorems for holomorphic curves in a complex Grassmann manifold G(3,6)

In this paper, we prove some local rigidity theorems of holomorphic curves in a complex Grassmann manifold [Formula: see text] by moving frames. By applying our rigidity theorems, we also give a characterization of all homogeneous holomorphic two-spheres in [Formula: see text] classified by the second author.

Rational homotopy of maps between certain complex Grassmann manifolds

LetGn,kdenote the complex Grassmann manifold ofk-dimensional vector subspaces of ℂn. Assumel,k≤ ⌊n/2⌋. We show that, for sufficiently largen, any continuous maph:Gn,l→Gn,kis rationally null homotopic if (i) 1 ≤k<l, (ii) 2 < l <k< 2(l− 1), (iii) 1 < l <k,ldividesnbutldoes not dividek.