Index T (X, Y ), 13 DD Is , 50 QC-hypersurface, 54 Ric, 18 Scal, 18 Sp(1), 9 Sp(n)-invariant parts, 9 Sp(n)Sp(1), 9 T 0 (X, Y ), 19 T 0 Q , 67 T 0 ξ i , 11 = T (ξ, .), 11 U(X, Y ), 19 [ . ][3][0], 38 [ . ] [sym][−1] , 38 Ψ+++, Ψ+−−, Ψ−+−, Ψ−−+, 9 G(H), 28, 39 αs, 17 ¯-pluriharmonic, 48 Q-orthonormal basis, 24 Q, 7 ρi, 18 σX,Y,Z, 20 τi, 18 ˜ 39 ζ i , 18 ds, 50 sp(1)-connection 1-forms, 17 u, 15 u Q , 67 3-Sasakian structure, 28 QC-vector fields, 69 3-contact automorphism, 64 3-contact manifold, 63 3-contact vector field, 64 ωi, 13 Sp(n), 9 fundamental 2-forms ωi, 13 symmetric part T 0 ξ i , 11 almost CR structures, 30 anti-CRF function, 55 anti-regular, 52 Bianchi identities, 24 Biquard connection, 10 canonical connection, 10 Casimir operator †, 9 Cayley transform, 74 conformal qc-automorphism, 65 conformal transformation, 37 curvature tensor R, 18 formally integrable, 29 HC structure, 29 HKT-manifolds, 52 horizontal divergence, 26, 71 horizontal gradient, 37 horizontal space, 7 hypercomplex manifold, 51 hyperhermitian contact, 29 hyperk¨ ahler metric, 28 infinitesimal conformal isometry, 65 infinitesimal isometry, 65 3-Sasakain, 67 Levi-Civita connection Dg, 17 Q-pluriharmonic, 50 QC manifold, 7 QC structure, 7 QC structure in dimension 7 , 10 QC vector field, 65 qc-Einstein, 23 qc-normal frame, 25 qc-pseudo-Einstein, 47 qc-Ricci tensor Ric, 18 qc-scalar curvature Scal, 18 qc-Yamabe equation, 38 G(H), 45 qc-Yamabe problem, 72 quaternionic anti-regular, 48, 50 quaternionic contact structure, 7 quaternionic Heisenberg group Siegel domain, 74 quaternionic Heisenberg group G(H), 28, 39 81
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