Session S23 - Group actions in Differential Geometry

Friday, July 16, 16:40 ~ 17:10 UTC-3

Killing forms on nilpotent Lie groups

Viviana del Barco

Universidade Estadual de Campinas, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Killing forms on Riemannian manifolds are differential forms whose covariant derivative with respect to the Levi-Civita connection is skew-symmetric. They generalize to higher degree the concept of Killing vector fields. Examples of Riemannian manifolds with non-trivial Killing k-forms are quite rare for k≥2. Nevertheless they appear, for instance, on nearly-Kähler manifolds, round spheres and Sasakian manifolds. The aim of this talk is to introduce recent results regarding the structure of 2-step nilpotent Lie groups endowed with left-invariant Riemannian metrics and carrying non-trivial Killing forms. In the way, we will review aspects of the Riemannian geometry of nilpotent Lie groups endowed with left-invariant metrics and describe the methods to achieve the structure results.

Joint work with Andrei Moroianu, CNRS-Université Paris Saclay, France.

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