# Details of talk

Title | Nearly Kaehler geometry, (2,3,5) distributions, and projective differential geometry. |
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Presenter | Rod Gover (University of Auckland) |

Author(s) | Prof Rod Gover |

Session | n/a |

Time | |

Abstract | 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 |