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TEMPERED HOMOGENEOUS SPACES IV
Journal of the Institute of Mathematics of Jussieu, 2022 AbstractLet G be a complex semisimple Lie group and H a complex closed connected subgroup. Let and be their Lie algebras. We prove that the regular representation of G in $L^2(G/H)$ is tempered if and only if the orthogonal of in contains regular elements by showing simultaneously the equivalence to other striking conditions, such as has a ...
Yves Benoist, Toshiyuki Kobayashi
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Tangent Bundles of Homogeneous Spaces are Homogeneous Spaces [PDF]
Proceedings of the American Mathematical Society, 1972 In this paper we describe how the tangent bundle of a homogeneous space can be viewed as a homogeneous space.
Brockett, R. W., Sussmann, H. J.
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Harmonic Maps into Homogeneous Spaces According to a Darboux Homogeneous Derivative [PDF]
, 2015 Our purpose is to use a Darboux homogenous derivative to understand the harmonic maps with values in homogeneous space. We present a characterization of these harmonic maps from the geometry of homogeneous space.
Santana, Alexandre J. +1 more
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Symplectic Homogeneous Spaces [PDF]
Transactions of the American Mathematical Society, 1974 It is proved in this paper that for a given simply connected Lie group G with Lie algebra g \mathfrak {g} , every left-invariant closed 2-form induces a symplectic homogeneous space. This fact generalizes the results in [7] and [12] that if H 1 (
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Symplectic homogeneous spaces [PDF]
Transactions of the American Mathematical Society, 1975 In this paper we make various remarks, mostly of a computational nature, concerning a symplectic manifold X on which a Lie group G acts as a transitive group of symplectic automorphisms. The study of such manifolds was initiated by Kostant [41 and Souriau [5] and was recently developed from a more general point of view by Chu [2].
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Minimal homogeneous submanifolds in euclidean spaces [PDF]
, 2002 We prove that minimal (extrinsically) homogeneous submanifolds of the Euclidean space are totally geodesic. As an application, we obtain that a complex (intrisecally) homogeneous submanifold of a complex Euclidean space must be totally ...
Di Scala, Antonio Jose'
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Polynomial dynamic and lattice orbits in S-arithmetic homogeneous spaces [PDF]
, 2009 Consider an homogeneous space under a locally compact group G and a lattice in G. Then the lattice naturally acts on the homogeneous space. Looking at a dense orbit, one may wonder how to describe its repartition. One then adopt a dynamical point of view
Guilloux, Antonin
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Rocky Mountain Journal of Mathematics, 1997 The authors prove that on a set with \(n>0\) elements there are up to homeomorphism \(\tau(n)\) homogeneous topologies. Here \(\tau(n)\) is the number of positive divisors of \(n\). They also prove that if \(X\) is finite and \(\tau\) is a connected homogeneous topology on \(X\) then \(\tau = \{\emptyset,X\}\).
Fora, Ali, Al-Bsoul, Adnan
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A homogeneous space whose complement is rigid [PDF]
, 2014 We construct a homogeneous subspace of $2^\omega$ whose complement is dense in $2^\omega$ and rigid. Using the same method, assuming Martin's Axiom, we also construct a countable dense homogeneous subspace of $2^\omega$ whose complement is dense in $2 ...
Medini, Andrea +2 more
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Homogeneous Ultrametric Spaces
Journal of Algebra, 1996 Fortsetzung von zwei vorangehenden Arbeiten über verallgemeinerte ultrametrische Räume [the authors, Generalized ultrametric spaces I, Abh. Math. Semin. Univ. Hamb. 66, 55-73 (1996); and Part II (1997)]. Es wird der Begriff des homogenen ultrametrischen Raumes eingeführt [the authors, C. R. Math. Acad. Sci., Soc. R. Can. 18, 1-16 (1996; Zbl 0853.54029)]
Priess-Crampe, S., Ribenboim, P.
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