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

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Details of talk

TitleLie algebroids and subgeometry
PresenterAnthony Blaom (University of Auckland)
Author(s)Dr Anthony Blaom

According to the Bonnet theorem, the metric and second fundamental
form of a surface in ${\mathbb R}^3 $ completely characterise the
surface, up to isometry. We explain how Lie algebroids arise naturally
in this old problem and present a new approach to proving Bonnet-type
theorems in the general setting of Klein geometries (conformal
geometry, projective geometry, CR geometry, etc). Our approach is
based on an infinitesimal characterization of smooth maps into a
homogeneous space which generalises \`Elie Cartan's characterization
of the smooth maps into a Lie group. No familiarity with Lie
algebroids will be assumed.