Differential Geometry Seminar: Nearly Kähler geometry and totally geodesic submanifolds

A theorem of Butruille asserts that the (simply connected, homogeneous) Riemannian manifolds of dimension six admitting a strict nearly Kähler metric are the round sphere S6, the space F(C3) of full flags in C3, the complex projective space CP3 and the almost product S3 x S3.

These spaces belong to the general class of naturally reductive homogeneous spaces, whose geometry can be understood in purely Lie-algebraic terms.

The aim of this talk is to describe a joint work with Alberto Rodríguez-Vázquez (KU Leuven) in which we classify the totally geodesic submanifolds of the aforementioned spaces. To this end, we will develop the algebraic tools needed to work with naturally reductive homogeneous spaces and to attack our problem, and later on we will exhibit the examples that appear in each case.

School of Computer and Mathematical Sciences