Naturality of homogeneous metrics on Stiefel manifolds SO ( m + 1 ) / SO ( m − 1 )

Naturality of homogeneous metrics on Stiefel manifolds SO ( m + 1 ) / SO ( m − 1 )

It is well known that the unit tangent sphere bundle T 1 S m of the standard sphere S m can be naturally identified with the Stiefel manifold V 2 R m + 1 = SO ( m + 1 ) / SO ( m − 1 ) . In this paper, we construct the ( 1 – 1 ) correspondence between all SO ( m + 1 ) -invariant homogeneous metrics o...

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Veröffentlicht in:Differential geometry and its applications 2010-04, Vol.28 (2), p.131-139
Hauptverfasser: Abbassi, Mohamed Tahar Kadaoui, Kowalski, Oldřich
Format: Artikel
Sprache:eng
Schlagworte:
Bundling
Construction
Differential geometry
g-natural metric
Manifolds
Mathematical analysis
Tangents
Unit tangent (sphere) bundle
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Zusammenfassung:It is well known that the unit tangent sphere bundle T 1 S m of the standard sphere S m can be naturally identified with the Stiefel manifold V 2 R m + 1 = SO ( m + 1 ) / SO ( m − 1 ) . In this paper, we construct the ( 1 – 1 ) correspondence between all SO ( m + 1 ) -invariant homogeneous metrics on V 2 R m + 1 and all so-called g-natural metrics on T 1 S m .
ISSN:0926-2245
1872-6984
DOI:10.1016/j.difgeo.2009.05.007