Nearly Kähler Geometry and $(2,3,5)$-Distributions via Projective Holonomy

Rod Gover, Roberto Panai, Travis Willse

We show that any dimension $6$ nearly Kähler (or nearly para-Kähler) geometry arises as a projective manifold equipped with a ${\text{G}}_2^{(\ast )}$ holonomy reduction. In the conver…