Symmetric Killing tensors on nilmanifolds

Abstract

We study left-invariant symmetric Killing 2-tensors on 2-step nilpotent Lie groups endowed with a left-invariant Riemannian metric, and construct genuine examples, which are not linear combinations of parallel tensors and symmetric products of Killing vector fields.

24 pages, v2 includes minor improvements

References in corpus (1)

• Open Problems, Questions, and Challenges in Finite-Dimensional Integrable Systems

Cited by in corpus (2)

• Higher degree Killing forms on $2-$step nilmanifolds
• First integrals on step-two and step-three nilpotent Lie groups