SO(n)\SO_0(n,1) has Positive Curvatures

Details SO(n)\SO_0(n,1) has Positive Curvatures SO(n)\SO_0(n,1) has Positive Curvatures

2010-12-02

arxiv.org/abs/1012.0357v1

Mathematics

Geometric Topology

Scientific paper

The Lie group SO_0(n, 1) has the left-invariant metric coming from the Killing-Cartan form. The maximal compact subgroup SO(n) of the isometry group acts from the left. The geometry of the quotient space of the homogeneous submersion SO_0(n, 1) -> SO(n)\SO_0(n, 1) is investigated. The space is expressed as a warped product. Its group of isometries and sectional curvatures are calculated.

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