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On Holonomy and Homogeneous Spaces [PDF]
Nagoya Mathematical Journal, 1957 In general a homogeneous space admits many invariant affine connections. Among these are certain connections which appear in many ways to be more natural than the others. We refer to the connections which K. Nomizu in [4] calls canonical affine connections of the first kind.
Bertram Kostant
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Strongly homogeneous spaces [PDF]
Proceedings of the American Mathematical Society, 1975 Spaces satisfying various conditions have previously been called strongly homogeneous spaces and many results about the group of homeomorphisms of such spaces have been proved. However spaces may satisfy some “strongly homogeneous” condition without being homogeneous.
Carol Kitai
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On the dimension of homogeneous spaces. [PDF]
Journal of the Mathematical Society of Japan, 1954 Tsuneyo Yamanoshita
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On Homogeneous Division of Space [PDF]
Proceedings of the Royal Society of London, 1894 1. The homogeneous division of any volume of space means the dividing of it into equal and similar parts, or cells, as I shall call them, all sameways oriented. If we take any point in the interior of one cell or on its boundary, and corresponding points of all the other cells, these points form a homogeneous assemblage of single points, according to ...
Lord Kelvin
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Curves in Homogeneous Spaces [PDF]
Canadian Journal of Mathematics, 1977 Let be a Lie group with connected Lie subgroup , and let M(t), N(i) be real analytic curves in , the Lie algebra of , with .
Ronald M. Hirschorn
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Homogeneous spaces of unsolvable Lie groups that do not admit equiaffine connections of nonzero curvature [PDF]
Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика, 2023 An important subclass among homogeneous spaces is formed by isotropically-faithful homogeneous spaces, in particular, this subclass contains all homogeneous spaces admitting invariant affine connection.
Mozhey, Natalya Pavlovna
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Harmonic analysis of functions almost periodic at infinity in Banach modules [PDF]
Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика, 2021 The article is devoted to homogeneous spaces of functions defined on a locally compact Abelian group and with their values in a complex Banach space.
Strukova, Irina Igorevna
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Left-Invariant Einstein-like Metrics on Compact Lie Groups
Mathematics, 2022 In this paper, we study left-invariant Einstein-like metrics on the compact Lie group G. Assume that there exist two subgroups, H⊂K⊂G, such that G/K is a compact, connected, irreducible, symmetric space, and the isotropy representation of G/H has exactly
An Wu, Huafei Sun
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Sobolev inequality with non-uniformly degenerating gradient
Electronic Journal of Qualitative Theory of Differential Equations, 2022 In this paper we prove the following weighted Sobolev inequality in a bounded domain $\Omega\subset \mathbb{R}^n$, $ n\geq 1$, of a homogeneous space $(\mathbb{R}^n, \rho, wdx)$, under suitable compatibility conditions on the positive weight functions $(
Farman Mamedov, Sara Monsurrò
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