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Weakly symmetric spaces and Riemannian g.o. spaces (Homogeneous Structures and Theory of Submanifolds)

Weakly symmetric spaces and Riemannian g.o. spaces (Homogeneous Structures and Theory of Submanifolds)
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Geodesics in Weakly Symmetric Spaces

Annals of Global Analysis and Geometry, 1997
A Riemannian manifold \(M\) is said to be weakly symmetric if for every two points \(p\) and \(q\) in \(M\) there is an isometry of \(M\) interchanging \(p\) and \(q\). The authors prove that every geodesic in a weakly symmetric space is an orbit of a one-parameter group of isometries of \(M\).
Oldrich Kowalski, Jürgen Berndt, Lieven Vanhecke   +2 more
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Weakly Symmetric Finsler Spaces

Communications in Contemporary Mathematics, 2010
In this paper, we introduce the notion of weakly symmetric Finsler spaces and study some geometrical properties of such spaces. In particular, we prove that each maximal geodesic in a weakly symmetric Finsler space is the orbit of a one-parameter subgroup of the full isometric group.
Zixin Hou
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On Weakly Symmetric Spaces

Acta Mathematica Hungarica, 2000
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Bandyopadhyay, S., De, U. C.
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On the Classification of Weakly Symmetric Finsler Spaces

Israel Journal of Mathematics, 2011
The first part of this paper is devoted to a general principle to classify non-Riemannian weakly symmetric Finsler spaces. Namely, if a connected manifold admits a weakly symmetric Finsler metric, then it admits also a weakly symmetric Riemannian metric.
Shaoqiang Deng
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Weakly Symmetric Spaces and Spherical Varieties

Transformation Groups, 1999
More than 40 years ago, \textit{A. Selberg} [J. Indian Math. Soc., New Ser. 20, 47-87 (1956; Zbl 0072.08201)] introduced weakly symmetric spaces \((M,g)\) in the following way. Let \((M,g)\) be a connected Riemannian manifold, \({\mathcal I}(M)\) its full isometry group, \(G\) a subgroup of \({\mathcal I}(M)\) acting transitively on \(M\), and \(u\) an
É B Vinberg
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Weakly Symmetric Spaces in Dimension Five

Journal of Geometry, 1997
A Riemannian manifold \((M,g)\) is said to be weakly symmetric if and only if, for any two points \(p,q\in M\), there exists an isometry of \(M\) interchanging \(p\) and \(q\). These manifolds have been introduced by Selberg who proved that the algebra of all isometry-invariant differential operators on such a space is a commutative algebra.
O Kowalski
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Weakly symmetric spaces and bounded symmetric domains

Transformation Groups, 1997
Let \((M= G/K,g)\) be a homogeneous Riemannian manifold and \(I(M,g)\) its isometry group. Following A. Selberg, \((M,g)\) is said to be weakly symmetric if there exists an element \(\mu\in I(M,g)\) satisfying \(\mu G\mu^{-1} =G\) and \(\mu^2 \in G\) such that for any given \(x,y \in M\), there exists a \(\gamma\in G\) such that \(\gamma x= \mu y\) and
Hiêú Nguyen
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An Algebraic Approach to Weakly Symmetric Finsler Spaces

Canadian Journal of Mathematics, 2010
AbstractIn this paper, we introduce a new algebraic notion, weakly symmetric Lie algebras, to give an algebraic description of an interesting class of homogeneous Riemann-Finsler spaces, weakly symmetric Finsler spaces. Using this new definition, we are able to give a classification of weakly symmetric Finsler spaces with dimensions 2 and 3.
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