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Nonpositively curved homogeneous spaces of dimension five / María Josefina Druetta.

By: Druetta, María Josefina, 1946-.
Material type: materialTypeLabelBookSeries: Trabajos de Matemática. Serie A / Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía y Física ; no.08.Publisher: Córdoba, Argentina : Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía y Física, 1991Description: 29 p. ; 30 cm.Subject(s): Differential geometry | Special Riemannian manifolds | Homogeneous manifolds | | Homogeneous spaces | Simply transitive isometry groups | Visibility axiom | Symemetric space | Geometría diferencial | Espacios homogeneos | Espacio simétricoSummary: We classify, in terms of the rank, the simply connected homogeneous spaces of nonpositive curvature and dimension five. In particular, an affirmative answer is given to the conjecture "An irreducible homogeneous spaces of nonpositive curvature and rank k ≥ 2 is a symmetric space of rank k". We exhibit examples in dimension five of rank one homogeneous spaces of nonpositive curvature having totally geodesic two-flats isometrically imbedded. Moreover, these examples show that the rank in a Lie group is not invariant under the change of left invariant metrics of nonpositive curvature.
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Bibliografía: p. 28-29.

We classify, in terms of the rank, the simply connected homogeneous spaces of nonpositive curvature and dimension five. In particular, an affirmative answer is given to the conjecture "An irreducible homogeneous spaces of nonpositive curvature and rank k ≥ 2 is a symmetric space of rank k".
We exhibit examples in dimension five of rank one homogeneous spaces of nonpositive curvature having totally geodesic two-flats isometrically imbedded. Moreover, these examples show that the rank in a Lie group is not invariant under the change of left invariant metrics of nonpositive curvature.

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