ADDENDUM TO OUR PAPER 'CONFORMAL MOTION OF CONTACT MANIFOLDS WITH CHARACTERISTIC VECTOR FIELD IN THE k-NULLITY DISTRIBUTION'

摘要

In [4], Okumura proved that if a Sasakian manifold M of dimension > 3, admits a non-isometric conformal motion v, then v is special concircular and hence, if, in addition, M is complete and connected, then it is isometric to a unit sphere. The last part of this result follows from Obata's theorem: A complete connected Riemannian manifold (M, g) of dimension > 1, admits a non-trivial solution ρ of partial differential equations ▽▽ρ = —c~2 ρg (for c = a constant > 0), if and only if M is isometric to a Euclidean sphere of radius 1/c. Recently, Sharma and Blair extended Okumura's result to dimension 3 assuming constant scalar curvature and proved the following: Let v be a non-isometric conformal motion on a 3-dimensional Sasakian manifold. If the scalar curvature of M is constant, then M is of constant curvature and v is special concircular.