Conjugate loci of totally geodesic submanifolds of symmetric spaces

Burns, J. M.

doi:10.1090/S0002-9947-1993-1091705-1

Conjugate loci of totally geodesic submanifolds of symmetric spaces
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Trans. Amer. Math. Soc. 337 (1993), 411-425 Request permission

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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