ﻻ يوجد ملخص باللغة العربية
Let $G$ be a connected, simply-connected, compact simple Lie group. In this paper, we show that the isometry group of $G$ with a left-invariant pseudo-Riemannan metric is compact. Furthermore, the identity component of the isometry group is compact if $G$ is not simply-connected.
The notion of $Gamma$-symmetric space is a natural generalization of the classical notion of symmetric space based on $Z_2$-grading of Lie algebras. In our case, we consider homogeneous spaces $G/H$ such that the Lie algebra $g$ of $G$ admits a $Gamm
We show that the compact quotient $Gammabackslashmathrm{G}$ of a seven-dimensional simply connected Lie group $mathrm{G}$ by a co-compact discrete subgroup $Gammasubsetmathrm{G}$ does not admit any exact $mathrm{G}_2$-structure which is induced by a left-invariant one on $mathrm{G}$.
We prove that there do not exist quasi-isometric embeddings of connected nonabelian nilpotent Lie groups equipped with left invariant Riemannian metrics into a metric measure space satisfying the RCD(0,N), with N > 1. In fact, we can prove that a sub
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 lef
We show that Lorentzian manifolds whose isometry group is of dimension at least $frac{1}{2}n(n-1)+1$ are expanding, steady and shrinking Ricci solitons and steady gradient Ricci solitons. This provides examples of complete locally conformally flat an