Über metrisch homogene räume

Dantzig, D. van

doi:10.1007/bf02940622

Cited by 66 publications

(50 citation statements)

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“…Furthermore, by a theorem of van Danzig and van der Waerden [8] and Lemma 4.5 we can conclude that ISO(X) and ISO m (X) are compact if X is compact.…”

Section: Moreover If Iso(x) Is a Lie Group Then Iso M (X) Is So As Wellmentioning

confidence: 78%

The Isometry Group of an RCD ∗ Space is Lie

Sosa

2017

Potential Anal

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We give necessary and sufficient conditions that show that both the group of isometries and the group of measure-preserving isometries are Lie groups for a large class of metric measure spaces. In addition we study, among other examples, whether spaces having a generalized lower Ricci curvature bound fulfill these requirements. The conditions are satisfied by RCD * -spaces and, under extra assumptions, by CD-spaces, CD * -spaces, and MCP-spaces. However, we show that the MCP-condition by itself is not enough to guarantee a smooth behavior of these automorphism groups.

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“…Furthermore, by a theorem of van Danzig and van der Waerden [8] and Lemma 4.5 we can conclude that ISO(X) and ISO m (X) are compact if X is compact.…”

Section: Moreover If Iso(x) Is a Lie Group Then Iso M (X) Is So As Wellmentioning

confidence: 78%

The Isometry Group of an RCD ∗ Space is Lie

Sosa

2017

Potential Anal

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“…But is that enough? A classical result of Dantzig and van der Waerden [7] says that the sphere with two handles does not possess a homogeneous metric although it is homogeneous in the topological sense. However, it admits a l.h.…”

Section: Unfortunately F M (X) Is Only a Very Small Part Of F(x)mentioning

confidence: 99%

Metrically invariant measures on locally homogeneous spaces and hyperspaces

Bandt¹,

Baraki²

1986

Pacific J. Math.

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“…Recently Yen determined their Betti numbers [139], using methods which involve knowledge of the representations of the groups (somewhat in the spirit of §12) and many additional pieces of information, in particular a conjectured formula of G. Hirsch about fibre bundles, when bundle and fibre have the homology structure of products of spheres (as Lie groups do, by Hopfs theorem). The dimensions of the primitive cocycles for the five groups are: (3,11), (3,11,15,23), (3,9,11,15,17,23), (3,11,15,19,23,27,35), (3,15,23,27,35,39,47,59). In the meantime Chevalley and Weil [26] have found a totally different approach to the whole problem, which made the computations for all groups much simpler.…”

Section: Weyps Theoremmentioning

confidence: 99%