标题： 弱复齐次空间 显示英文标题

标题： Weakly complex homogeneous spaces

摘要： 我们通过填补一个之前未解决的情况，完成了对具有弱复切丛的紧致内对称空间的最近分类，并将此分类扩展到具有正欧拉示性数的紧致齐次空间更大类别中。 我们证明，一个单连通的紧等阶齐次空间具有弱复切丛当且仅当它是紧等阶齐次空间的乘积，这些空间要么携带不变的几乎复结构（并由Hermann分类），要么具有稳定平凡的切丛（并由Singhof和Wemmer分类），或者属于一个明确列出的弱复空间，这些空间既没有稳定平凡的切丛，也不携带不变的几乎复结构。 显示英文摘要

摘要： We complete our recent classification of compact inner symmetric spaces with weakly complex tangent bundle by filling up a case which was left open, and extend this classification to the larger category of compact homogeneous spaces with positive Euler characteristic. We show that a simply connected compact equal rank homogeneous space has weakly complex tangent bundle if and only if it is a product of compact equal rank homogeneous spaces which either carry an invariant almost complex structure (and are classified by Hermann), or have stably trivial tangent bundle (and are classified by Singhof and Wemmer), or belong to an explicit list of weakly complex spaces which have neither stably trivial tangent bundle, nor carry invariant almost complex structures.