S-~ 1 ¡Á S ~ 7 A Class Of Local Conformal K (?) Hler Metrics

Let A ∈ GL(4,C)be a diagonal linear matrix with all eigenvalues satisfying | α_i| > 1,1 ≤ i ≤ 4. M = (C~n - 0) \ is Hopf manifold with locally conformally Kahler metric and it is diffeomorphic to s~1 x s~7. In this paper, the main results are as following1 )The global vector fields which have a better property are constructed on s~1 xs~7. We pull the complex structure of Hopf manifold onto s~1 x s~7, which makes the complex structure clear on the vectors fields.2) We construct a locally conformally Kahler metric on s~1 x s~7,which makes the metric clear on the vectors fields.3) On s7, we get conditions which could make the locally conformal Kahler metric equate to the metric of deformation of canonical Sasakian structure.