Document Zbl 1058.53041

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The exceptional compact symmetric spaces \(G_2\) and \(G_2/\text{SO}(4)\) as tubes. (English) Zbl 1058.53041

Monatsh. Math. 141, No. 4, 323-335 (2004).

The author studies cohomogeneity one actions of \(\text{SU}(3)\times \text{SU}(3)\) on the exceptional Lie group \(G_2\) and of \(\text{SU}(3)\) on the symmetric space \(G_2/\text{SO}(4)\). He computes the principal curvatures of the principal orbits and rederives the volume of \(G_2\) and \(G_2/\text{SO}(4)\).

Reviewer: Thomas Püttmann (Bochum)

Cited in 2 Documents

MSC:

53C35	Differential geometry of symmetric spaces
57S15	Compact Lie groups of differentiable transformations
53C40	Global submanifolds

Keywords:

symmetric spaces; cohomogeneity one actions; exceptional Lie groups

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