Harmonic Vector Fields

4.3. Stability of the Reeb Vector Field

Few results concerning the stability of the Reeb vector field are known so far. E. Boeckx & J.C. Gonzales-Davila & L. Vanhecke, [56] , studied the stability of the Reeb vector underlying the standard contact metric structure on S ( M ) when M is a compact quotient of a two-point homogeneous space. V. Borrelli, [61] , studied the stability of the Reeb vector field of an arbitrary Sasakian manifold. Precisely

Theorem 4.38 V. Borrelli, [61]

Let ( M , ( ϕ , ξ , η , g )) be a compact Sasakian manifold and

Then

i. Assume that ξ is stable with respect to the energy functional E. Then there is such that is stable ...