arXiv subjects
Publications and source records attributed to Huibin Chen.
We prove that the torsion three-form in the preferred splitting of a left-invariant generalized nilsoliton on a nilpotent Lie group is harmonic. This gives a positive answer to Question 7.12 proposed by Fusi-Lafuente-Stanfield in [3].
In this paper, we focus on homogeneous spaces which are constructed from two strongly isotropy irreducible spaces, and prove that any geodesic orbit metric on these spaces is naturally reductive.
In this paper, we investigate left-invariant geodesic orbit metrics on connected simple Lie groups, where the metrics are formed by the structures of generalized flag manifolds. We prove that all these left-invariant geodesic orbit metrics on simple Lie groups are naturally reductive.
In this article, we achieved several non-naturally reductive Einstein metrics on exceptional simple Lie groups, which are formed by the decomposition arising from general Wallach spaces. By using the decomposition corresponding to the two involutive automorphisms, we calculated the non-zero coefficients in the expression for the components of Ricci tensor with respect to the given metrics. The Einstein metrics are obtained as solutions of systems polynomial equations, which we manipulate by symbolic computations using Gröbner bases.
In this article, we prove that every compact simple Lie group $SO(n)$ for $n\geq 10$ admits at least $2\left([\frac{n-1}{3}]-2\right)$ non-naturally reductive left-invariant Einstein metrics.
In the paper "Einstein metrics on compact simple Lie groups attached to standard triples", the authors introduced the definition of standard triples and proved that every compact simple Lie group $G$ attached to a standard triple $(G,K,H)$ admits a left-invariant Einstein metric which is not naturally reductive except the standard triple $(\Sp(4),2\Sp(2),4\Sp(1))$. For the triple $(\Sp(4),2\Sp(2),4\Sp(1))$, we find there exists an involution pair of $\sp(4)$ such that $4\sp(1)$ is the fixed point of the pair, and then give the decomposition of $\sp(4)$ as a direct sum of irreducible $\ad(4\sp(1))$-modules. But $\Sp(4)/4\Sp(1)$ is not a generalized Wallach space. Furthermore we give left-invariant Einstein metrics on $\Sp(4)$ which are non-naturally reductive and $\Ad(4\Sp(1))$-invariant. For the general case $(\Sp(2n_1n_2),2\Sp(n_1n_2),2n_2\Sp(n_1))$, there exist $2n_2-1$ involutions of $\sp(2n_1n_2)$ such that $2n_2\sp(n_1))$ is the fixed point of these $2n_2-1$ involutions, and it follows the decomposition of $\sp(2n_1n_2)$ as a direct sum of irreducible $\ad(2n_2\sp(n_1))$-modules. In order to give new non-naturally reductive and $\Ad(2n_2\Sp(n_1)))$-invariant Einstein metrics on $\Sp(2n_1n_2)$, we prove a general result, i.e. $\Sp(2k+l)$ admits at least two non-naturally reductive Einstein metrics which are $\Ad(\Sp(k)\times\Sp(k)\times\Sp(l))$-invariant if $k<l$. It implies that every compact simple Lie group $\Sp(n)$ for $n\geq 4$ admits at least $2[\frac{n-1}{3}]$ non-naturally reductive left-invariant Einstein metrics.