New examples of Riemannian g.o. manifolds in dimension 7

Dušek, Zdeněk; Kowalski, Oldřich; Nikčević, Stana

doi:10.1016/j.difgeo.2004.03.006

Cited by 41 publications

(44 citation statements)

References 7 publications

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“…For the examples of geodesic graphs of various degrees we refer to [3], [7], [11]. The systematic description of contemporary results for Riemannian g.o.…”

Section: Homogeneous Geodesics and Geodesic Graphsmentioning

confidence: 99%

“…manifolds was given in [7]. spaces considered in [11] and [7]. It was the first example of an almost g.o.…”

Section: Homogeneous Geodesics and Geodesic Graphsmentioning

confidence: 99%

“…It was the first example of an almost g.o. For the new 7-dimensional examples, we used a modification similar to the Riemannian 7-dimensional example constructed in [7]. In Section 3 of the present work we show other 6-dimensional and 7-dimensional examples which can be obtained by modifications of g.o.…”

Section: Homogeneous Geodesics and Geodesic Graphsmentioning

confidence: 99%

“…In [4], the 6-dimensional and 7-dimensional pseudo-Riemannian g.o. spaces considered in [13], [11] and [7]. These examples are the modifications of Riemannian g.o.…”

Section: Introductionmentioning

confidence: 99%

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Almost g.o. spaces in dimensions 6 and 7

Dušek

2008

Advg

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“…For the examples of geodesic graphs of various degrees we refer to [3], [7], [11]. The systematic description of contemporary results for Riemannian g.o.…”

Section: Homogeneous Geodesics and Geodesic Graphsmentioning

confidence: 99%

“…manifolds was given in [7]. spaces considered in [11] and [7]. It was the first example of an almost g.o.…”

Section: Homogeneous Geodesics and Geodesic Graphsmentioning

confidence: 99%

Section: Homogeneous Geodesics and Geodesic Graphsmentioning

confidence: 99%

“…In [4], the 6-dimensional and 7-dimensional pseudo-Riemannian g.o. spaces considered in [13], [11] and [7]. These examples are the modifications of Riemannian g.o.…”

Section: Introductionmentioning

confidence: 99%

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Almost g.o. spaces in dimensions 6 and 7

Dušek

2008

Advg

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“…For many results and further references on Riemannian g.o. manifolds see for example [1,6,9,12,17]. The basic formula characterizing geodesic vectors in the Riemannian case was derived in [17]: A vector X ∈ g is geodesic if and only if [X, Z] m , X m = 0 for all Z ∈ m .…”

Section: Introductionmentioning

confidence: 99%

Homogeneous Geodesics in Homogeneous Affine Manifolds

2009

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For studying homogeneous geodesics in Riemannian and pseudoRiemannian geometry (on reductive homogeneous spaces) there is a simple algebraic formula which involves the reductive decomposition g = h +m of the Lie algebra g of the isometry group G and the scalar product on m induced by the metric. In the affine differential geometry, there is not such a universal formula. In the present paper, we propose a simple method of investigation of affine homogeneous geodesics. As an application, we describe homogeneous geodesics for homogeneous affine connections in dimension 2 and we find families of affine g.o. spaces in dimension 2. We also solved the problem of the canonical re-parametrization of affine homogeneous geodesics. Mathematics Subject Classification (2000). 53B05, 53C30.

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Some Finsler spaces with homogeneous geodesics

Yan

2016

Mathematische Nachrichten

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A geodesic in a homogeneous Finsler space (G/H,F) is called a homogeneous geodesic if it is an orbit of a one‐parameter subgroup of G. A homogeneous Finsler space (G/H,F) 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. spaces to the Finslerian setting. In the present paper, we investigate homogeneous geodesics in homogeneous (α,β) spaces, and obtain the sufficient and necessary condition for an (α,β) space to be a g.o. space. As an application, we get a series of new examples of Finsler g.o. spaces.

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New examples of Riemannian g.o. manifolds in dimension 7

Cited by 41 publications

References 7 publications

Almost g.o. spaces in dimensions 6 and 7

Almost g.o. spaces in dimensions 6 and 7

Homogeneous Geodesics in Homogeneous Affine Manifolds

Some Finsler spaces with homogeneous geodesics

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