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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the singularity of the exponential map on a Lie group


Author: Heng Lung Lai
Journal: Proc. Amer. Math. Soc. 62 (1977), 334-336
MSC: Primary 22E60
MathSciNet review: 0432823
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0432823-4
PII: S 0002-9939(1977)0432823-4
Article copyright: © Copyright 1977 American Mathematical Society