Weakly complex inner symmetric spaces

Abstract

We prove that the tangent bundle of an inner symmetric space $M$ of compact type is weakly complex if and only if $M$ is a Riemannian product $M_1\times ...\times M_k$, each $M_i$ being an even-dimensional round sphere or Hermitian symmetric.

The manuscript was withdrawn since it was merged into the related article arXiv:1003.5172