Differential Geometry, Lie Theory and Low-Dimensional Topology, Melbourne, Australia, 2016

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Details of talk

TitleNearly Kaehler geometry, (2,3,5) distributions, and projective differential geometry.
PresenterRod Gover (University of Auckland)
Author(s)Prof Rod Gover

Nearly Kaehler geometries are one of the most important classes in the
celebrated Gray-Hervella classification of almost Hermitian
geometries.  A Cartan (2, 3, 5)-distribution is the geometry arising
from a maximally nondegenerate distribution of 2-planes in the tangent
bundle of a 5-manifold.  We reveal a beautiful picture of how any 
(2, 3, 5)-geometry arises as the induced geometry on the boundary at infinity
of a nearly Kaehler manifold; included is an explanation of how the
almost complex structure of the nearly Kaehler geometry degenerates at
the boundary to yield there the distribution generating the (2, 3, 5)
structure. This uses the algebraic structure of the imaginary (split)
octonions, and also new results and ideas from the general theory of
Cartan holonomy reduction (as applied to projective geometry).

This is based on joint work with Roberto Panai and Travis Willse.

Rod Gover