论文标题
从溶胶到双曲线空间的插值
An Interpolation from Sol to Hyperbolic Space
论文作者
论文摘要
我们研究了一个非同态溶解谎言组的单参数家族，当配备规范的左转量指标时，$$ ds^2 = e^{ - 2z} dx^2+e^{2αz} dy^2+dz^2+dz^2+dz^2 $$从一个模型的模型中插入了一个模型，该模型是一个模型的模型， $ \ mathbb {h}^2 \ times \ mathbb {r} $。这些谎言组也是带有正交坐标的VI类的比安奇组。作为与理查德·施瓦茨（Richard Schwartz）在SOL上的联合合作的延续，我们主要在插值中以一些积极的截面曲率分析了这些谎言组。我们的主要结果是在最大化标量曲率的组身份处的切割基因座的表征。
We study a one-parameter family of nonisomorphic solvable Lie groups, which, when equipped with canonical left-invariant metrics, $$ds^2=e^{-2z}dx^2+e^{2αz}dy^2+dz^2$$ becomes an interpolation from a model of the Sol geometry to a model of Hyperbolic Space, with a stop at $\mathbb{H}^2\times \mathbb{R}$. These Lie groups are also Bianchi groups of Type VI with orthogonal coordinates. As a continuation of joint work with Richard Schwartz on Sol, we primarily analyze those Lie groups in our interpolation with some positive sectional curvature. Our main result is a characterization of the cut locus at the identity of the group that maximizes scalar curvature.
