4 problems

Let $G$ be a complex simple Lie group and let $P\subset G$ be a maximal parabolic subgroup. Assume that $G/P$ is not a compact Hermitian symmetric space, or, if $G/P$ is a compact…

Let $M$ be a closed Lorentzian conformal manifold. It is essential if its conformal transformation group does not preserve any metric in the conformal class. Lorentzian Lichnerowic…

Let $H$ be a distribution with co-rank $s$ and rank $r$, so that its derived distribution satisfies $[H,H]=T$ and hence $s<r(r-1)/2$. Square-root growth conjecture. The minimal pos…

Let $G$ be the split real form of a semisimple Lie group with parabolic subgroup $P$, and let $P\to E\to M$ be a $G/P$-geometry. Suppose that the Lie algebra $\mathfrak{g}$ has its…