A remark on left invariant metrics on compact Lie groups
✍ Scribed by Lorenz J. Schwachhöfer
- Publisher
- Springer
- Year
- 2008
- Tongue
- English
- Weight
- 119 KB
- Volume
- 90
- Category
- Article
- ISSN
- 0003-889X
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## Abstract For each simply connected three‐dimensional Lie group we determine the automorphism group, classify the left invariant Riemannian metrics up to automorphism, and study the extent to which curvature can be altered by a change of metric. Thereby we obtain the principal Ricci curvatures, t
We describe left-invariant affine structures that is, left-invariant flat torsion-free . affine connections ٌ on reductive linear Lie groups G. They correspond bijectively to LSA-structures on the Lie algebra ᒄ of G. Here LSA stands for left-symmetric algebra. If ᒄ has trivial or one-dimensional cen