Left-invariant Einstein metrics on S3 x S3

Florin Belgun, Vicente Cortés, Alexander S. Haupt, David Lindemann

In arXiv:1703.10512 we continued the classification of homogeneous compact Einstein manifolds in dimension six. We considered the remaining open case, namely left-invariant Einstein metrics g on G=S3 x S3 together with the simplifying assumption that the isotropy group K of g in the group of motions is non-trivial. When K≠Z2 we prove that the Einstein metrics on G are given by (up to homothety) either the standard metric or the nearly Kähler metric, based on representation-theoretic arguments and computer algebra. For the remaining case K=Z2 we present partial results.

The corresponding data, which consists of the input and output files of the computer-based Gröbner basis computations, is contained in the following files: