Results 131 to 140 of about 1,691 (159)

Geodesic symmetries of homogeneous K�hler Manifolds

Geometriae Dedicata, 1981
D'Atri and Nickerson [6], [7] have given necessary conditions for the geodesic symmetries of a Riemannian manifold to preserve the volume element. We use their results to show that ifG is a compact simple Lie group,T is a maximal torus ofG, andG/T is not symmetric, then anyG-invariant Kahler metric onG/T does not have volume-preserving geodesic ...
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Geodesics and Jacobi Fields in Bounded Homogeneous Domains

Proceedings of the American Mathematical Society, 1983
The authors study bounded homogeneous domains in \({\mathbb{C}}^ n\) endowed with the Bergman metric. In case D is symmetric it is well known that the sectional curvature is nonpositive, and as a consequence D has no focal points (in the sense that any nontrivial Jacobi field along a nontrivial geodesic \(\gamma\) vanishing at \(\gamma\) (0) has ...
D'Atri, J. E., Zhao, Yanda
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Homogeneous Lorentzian Spaces Whose Null-geodesics are Canonically Homogeneous

Letters in Mathematical Physics, 2006
A homogeneous Lorentzian space is said to be a null geodesic orbit-space, if all null geodesics are homogeneous. The aim of this paper is to show that the null geodesic orbit-spaces for which all geodesic vectors are canonical admit a non-vanishing homogeneous Lorentzian structure belonging to the class \(T_1\oplus T_3\).
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HOMOGENEOUS SPACES OF NONPOSITIVE CURVATURE AND THEIR GEODESIC FLOW

International Journal of Mathematics, 1995
Consider the geodesic flow on the unit tangent bundle SH of a 1-connected, irreducible homogeneous space H of nonpositive curvature. We prove that any flow invariant, isometry invariant C0-function on SH is necessarily constant, unless H is symmetric of higher rank.
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Some Finsler spaces with homogeneous geodesics

Mathematische Nachrichten, 2016
A geodesic in a homogeneous Finsler space is called a homogeneous geodesic if it is an orbit of a one‐parameter subgroup of G. A homogeneous Finsler space is called Finsler g.o. space if its all geodesics are homogeneous. Recently, the author studied Finsler g.o. spaces and generalized some geometric results on Riemannian g.o.
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Geodesic orbit metrics on homogeneous spaces constructed by strongly isotropy irreducible spaces

Science China Mathematics, 2021
Huibin Chen, Chen Zhiqi
exaly  

Totally geodesic orbits in homogeneous spaces

1996
Let M = G/H be a homogeneous space with G a compact, connected Lie group, H С G a closed subgroup and π : G →+ G/H the canonical projection. Let K С G be a closed subgroup and K(o) the orbit of o = π(H), under the restriction of α to K. Put dimK(o) = n.
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Closed geodesics on homogeneous spaces

Mathematische Zeitschrift, 1976
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HOMOGENEITY AND ISOTROPY IN GEODESIC SPACES

The Quarterly Journal of Mathematics, 1958
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Standard homogeneous (α1,α2)${\big(\alpha _1,\alpha _2\big)}$‐metrics and geodesic orbit property

Mathematische Nachrichten, 2022
Ming Xu
exaly