2 problems

Let $G_\mathbb{C}/K_\mathbb{C}$ be an irreducible complex symmetric space, where $G_\mathbb{C}$ is a complex semisimple Lie group and $K_\mathbb{C}$ is the fixed-point subgroup of…

Let $n$ be a positive integer, and let $SO(n+1,\mathbb{C})/SO(n,\mathbb{C})$ be the $n$-dimensional complex sphere. Kobayashi's complex sphere conjecture. The complex sphere admits…