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Transactions of the American Mathematical Society

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Conjugate loci of totally geodesic submanifolds of symmetric spaces


Author: J. M. Burns
Journal: Trans. Amer. Math. Soc. 337 (1993), 411-425
MSC: Primary 53C35; Secondary 53C20, 53C40
DOI: https://doi.org/10.1090/S0002-9947-1993-1091705-1
MathSciNet review: 1091705
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Abstract: The conjugate and cut loci of fixed point sets of involutions which fix the origin of a compact symmetric space are studied. The first conjugate locus is described in terms of roots and weights of certain representations. When the first conjugate locus and the cut locus agree, we study Morse functions which give a simple decomposition of the symmetric space. We describe for some examples the topological implications of our results.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1993-1091705-1
Article copyright: © Copyright 1993 American Mathematical Society

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