On the singularity of the exponential map on a Lie group
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- by Heng Lung Lai PDF
- Proc. Amer. Math. Soc. 62 (1977), 334-336 Request permission
Abstract:
Let $\mathfrak {G}$ be a connected (real or complex) Lie group with Lie algebra G. Define a conjugate point g of $\mathfrak {G}$ as a point $g = \exp x$ for some $x \in G$ and $d{\exp _x}$ is a noninvertible linear map. We prove that $g \in \mathfrak {G}$ is a conjugate point if and only if $g = \exp {x_\lambda }$ for at least a (complex parameter) family of elements ${x_\lambda }(\lambda \in {\mathbf {C}})$ in G.References
- J. Dixmier, L’application exponentielle dans les groupes de Lie résolubles, Bull. Soc. Math. France 85 (1957), 113–121 (French). MR 92930
- Sigurđur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962. MR 0145455
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 62 (1977), 334-336
- MSC: Primary 22E60
- DOI: https://doi.org/10.1090/S0002-9939-1977-0432823-4
- MathSciNet review: 0432823