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Geodesic completeness of pseudo and holomorphic Riemannian metrics on Lie groups
- Publication Year :
- 2022
-
Abstract
- This paper is devoted to geodesic completeness of left-invariant metrics for real and complex Lie groups. We start by establishing the Euler-Arnold formalism in the holomorphic setting. We study the real Lie group $\mathrm{SL}(2, \mathbb{R})$ and reobtain the known characterization of geodesic completeness and, in addition, present a detailed study where we investigate the maximum domain of definition of every single geodesic for every possible metric. We investigate completeness and semicompleteness of the complex geodesic flow for left-invariant holomorphic metrics and, in particular, establish a full classification for the Lie group $\mathrm{SL}(2, \mathbb{C})$.<br />Comment: 34 pages, 18 figures
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2208.10873
- Document Type :
- Working Paper