Compact Riemannian Manifolds with Homogeneous Geodesics

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2009
• Main Authors: Alekseevsky, D.V., Nikonorov, Y.G.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2009
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/149121
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Compact Riemannian Manifolds with Homogeneous Geodesics / D.V. Alekseevsky, Y.G. Nikonorov // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 28 назв. — англ.

A homogeneous Riemannian space (M = G/H,g) is called a geodesic orbit space (shortly, GO-space) if any geodesic is an orbit of one-parameter subgroup of the isometry group G. We study the structure of compact GO-spaces and give some sufficient conditions for existence and non-existence of an invaria...