The crystal and molecular structure of 9-methylphenanthro[4,3-a]dibenzothiophene

The crystal structure of 9-methylphenanthro[4,3-a]dibenzothiophene, C₂₅H₁₆S, M_r = 348.47, has been determined. Monoclinic, P2₁/c, a = 11.364(3), b, = 14.257(3), c = 11.575(2)Å, β = 116.26(2)°, V = 1681.9(7)ų, Z = 4, D_x = 1.38 g/cc, MoKα radiation λ = .71069 Å, F(000) = 728, T = 163K, R = .0458 for 2330 reflections. The structure compares favorably with that of hexahelicene and methylated derivatives. The thiophene moiety increases the helical core radius and decreases the pitch with respect to hexahelicene and its derivatives.     

Almost Extrinsically Homogeneous Submanifolds of Euclidean Space

Consider a closed manifold M immersed in R^m. Suppose that the trivial bundle M × R^m = T M ⊗ ν M is equipped with an almost metric connection ~ ∇ which almost preserves the decomposition of M × R^m into the tangent and the normal bundle. Assume moreover that the difference Γ = ∂~∇ with the usual derivative ∂ in R^m is almost ~∇-parallel. Then M admits an extrinsically homogeneous immersion into R^m. Mathematics Subject Classifications (2000): 53C20, 53C24, 53C30, 53C42, 53C40.