SO(n)\SO_0(n,1) has Positive Curvatures
Taechang Byun, Kyeonghee Jo, Kyung Bai Lee
TL;DR
This paper investigates the geometric properties of the Lie group SO_0(n, 1) with a specific metric, analyzing its quotient space, isometries, and sectional curvatures, revealing insights into its positive curvature characteristics.
Contribution
It provides a detailed analysis of the quotient space of SO_0(n, 1), expressing it as a warped product and computing its isometry group and sectional curvatures, highlighting positive curvature features.
Findings
The quotient space can be expressed as a warped product.
The isometry group of the quotient space is characterized.
Sectional curvatures of the space are computed, showing positive curvature regions.
Abstract
The Lie group SO_0(n, 1) has the left-invariant metric coming from the Killing-Cartan form. The maximal compact subgroup SO(n) of the isometry group acts from the left. The geometry of the quotient space of the homogeneous submersion SO_0(n, 1) -> SO(n)\SO_0(n, 1) is investigated. The space is expressed as a warped product. Its group of isometries and sectional curvatures are calculated.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Differential Geometry Research · Geometric Analysis and Curvature Flows