Mingming Ren | Searcharxiv

arXiv2011

The decomposition of a Lie group with a left invariant pseudo-Riemannian metric and the uniqueness

In this paper, we discuss the decomposition of a Lie group with a left invariant pseudo-Riemannian metric and the uniqueness. In fact, it is a decomposition of a Lie group into totally geodesic sub-manifolds which is different from the De Rham decomposition on a Lie group. As an application, we give a decomposition of a Lie group with a left invariant pseudo-Riemannian Einstein metric, and prove that the decomposition is unique up to the order of the parts in the decomposition.

math.GR↗

arXiv2010

Classification of $(n+3)$-dimensional metric $n$-Lie algebras

In this paper, we focus on $(n+3)$-dimensional metric $n$-Lie algebras. To begin with, we give some properties on $(n+3)$-dimensional $n$-Lie algebras. Then based on the properties, we obtain the classification of $(n+3)$-dimensional metric $n$-Lie algebras.

math-ph↗