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ON HOMOGENEOUS SQUARE EINSTEIN METRICS
Deng, Shaoqiang,Liu, Xingda Korean Mathematical Society 2017 대한수학회보 Vol.54 No.3
We prove that a homogeneous square Einstein Finsler metric is either Riemannian or flat.
On homogeneous square Einstein metrics
Shaoqiang Deng,Xingda Liu 대한수학회 2017 대한수학회보 Vol.54 No.3
We prove that a homogeneous square Einstein Finsler metric is either Riemannian or flat.
Nilpotency of the Ricci operator of pseudo-Riemannian solvmanifolds
Huihui An,Shaoqiang Deng,Zaili Yan 대한수학회 2024 대한수학회보 Vol.61 No.3
A pseudo-Riemannian solvmanifold is a solvable Lie group endowed with a left invariant pseudo-Riemannian metric. In this short note, we investigate the nilpotency of the Ricci operator of pseudo-Rie\-mannian solvmanifolds. We focus on a special class of solvable Lie groups whose Lie algebras can be expressed as a one-dimensional extension of a nilpotent Lie algebra $\mathbb{R}D\ltimes \mathfrak{n}$, where $D$ is a derivation of $\mathfrak{n}$ whose restriction to the center of $\mathfrak{n}$ has at least one real eigenvalue. The main result asserts that every solvable Lie group belonging to this special class admits a left invariant pseudo-Riemannian metric with nilpotent Ricci operator. As an application, we obtain a complete classification of three-dimensional solvable Lie groups which admit a left invariant pseudo-Riemannian metric with nilpotent Ricci operator.