Elliptic isometries of the manifold of positive definite real matrices with the trace metric. (English) Zbl 1466.53059
Summary: We study the differential-geometric properties of the loci of fixed points of the elliptic isometries of the manifold of positive definite real matrices with the trace metric. We also give an explicit description of such loci and in particular we find their De Rham decomposition.
MSC:
| 53C35 | Differential geometry of symmetric spaces |
| 15B48 | Positive matrices and their generalizations; cones of matrices |
Keywords:
positive definite matrices; trace metric; Hadamard manifolds; (elliptic) isometries; (irreducible) symmetric Riemannian spaces; de Rham decompositionReferences:
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