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- W3148734358 abstract "We propose studies of special Riemannian geometries with structure groups H1 = SO(3) ⊂ SO(5), H2 = SU(3) ⊂ SO(8), H3 = Sp(3) ⊂ SO(14) and H4 = F4 ⊂ SO(26) in respective dimensions 5, 8, 14 and 26. These geometries, have torsionless models with symmetry groups G1 = SU(3), G2 = SU(3)×SU(3), G3 = SU(6) and G4 = E6. The groups Hk and Gk constitute a part of the ‘magic square’ for Lie groups. Apart from the Hk geometries in dimensions nk, the ‘magic square’ Lie groups suggest studies of a finite number of other special Riemannian geometries. Among them the smallest dimensional are U(3) geometries in dimension 12. The other structure groups for these Riemannian geometries are: S(U(3) × U(3)), U(6), E6 × SO(2), Sp(3)×SU(2), SU(6)×SU(2), SO(12)×SU(2) and E7×SU(2). The respective dimensions are: 18, 30, 54, 28, 40, 64 and 112. This list is supplemented by the two ‘exceptional’ cases of SU(2) × SU(2) geometries in dimension 8 and SO(10)× SO(2) geometries in dimension 32. MSC classification: 53A40, 53B15, 53C10" @default.
- W3148734358 created "2021-04-13" @default.
- W3148734358 creator A5063787799 @default.
- W3148734358 date "2006-01-01" @default.
- W3148734358 modified "2023-09-23" @default.
- W3148734358 title "SPECIAL RIEMANNIAN GEOMETRIES MODELED ON THE DISTINGUISHED SYMMETRIC SPACES" @default.
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