Compact Riemannian manifolds with homogeneous geodesics.

Alekseevsky, Dmitrii V.; Nikonorov, Yurii G.

Displaying similar documents to “Compact Riemannian manifolds with homogeneous geodesics.”

On the set of homogeneous geodesics of a left-invariant metric.

Szenthe, János (2002)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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Adapted complex structures and Riemannian homogeneous spaces

Róbert Szőke (1998)

Annales Polonici Mathematici

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We prove that every compact, normal Riemannian homogeneous manifold admits an adapted complex structure on its entire tangent bundle.

Metrics with homogeneous geodesics on flag manifolds

Dimitri V. Alekseevsky, Andreas Arvanitoyeorgos (2002)

Commentationes Mathematicae Universitatis Carolinae

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A geodesic of a homogeneous Riemannian manifold $(M = G / K, g)$ is called homogeneous if it is an orbit of an one-parameter subgroup of $G$ . In the case when $M = G / H$ is a naturally reductive space, that is the $G$ -invariant metric $g$ is defined by some non degenerate biinvariant symmetric bilinear form $B$ , all geodesics of $M$ are homogeneous. We consider the case when $M = G / K$ is a flag manifold, i.eȧn adjoint orbit of a compact semisimple Lie group $G$ , and we give a simple necessary condition that $M$ admits a non-naturally...

A property of Wallach's flag manifolds

Teresa Arias-Marco (2007)

Archivum Mathematicum

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In this note we study the Ledger conditions on the families of flag manifold $(M^{6} = S U (3) / S U (1) \times S U (1) \times S U (1), g_{(c_{1}, c_{2}, c_{3})})$ , $(M^{12} = S p (3) / S U (2) \times S U (2) \times S U (2), g_{(c_{1}, c_{2}, c_{3})})$ , constructed by N. R. Wallach in (Wallach, N. R., Compact homogeneous Riemannian manifols with strictly positive curvature, Ann. of Math. 96 (1972), 276–293.). In both cases, we conclude that every member of the both families of Riemannian flag manifolds is a D’Atri space if and only if it is naturally reductive. Therefore, we finish the study of $M^{6}$ made by D’Atri and Nickerson in (D’Atri, J. E., Nickerson,...

Riemannian symmetries in flag manifolds

Paola Piu, Elisabeth Remm (2012)

Archivum Mathematicum

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Flag manifolds are in general not symmetric spaces. But they are provided with a structure of $ℤ_{2}^{k}$ -symmetric space. We describe the Riemannian metrics adapted to this structure and some properties of reducibility. The conditions for a metric adapted to the $ℤ_{2}^{2}$ -symmetric structure to be naturally reductive are detailed for the flag manifold $S O (5) / S O (2) \times S O (2) \times S O (1)$ .