A classification of 3-dimensional contact metric manifolds with \(Q\phi =\phi Q\). II. (English) Zbl 0767.53023
Summary: [For part I, cf. the first author, Th. Koufogiorgos and R. Sharma, Kodai Math. J. 13, No. 3, 391-401 (1990; Zbl 0716.53041).]
It is shown that a 3-dimensional contact metric manifold on which \(Q\phi=\phi Q\) is either Sasakian, flat or locally isometric to a left invariant metric on the Lie group \(SU(2)\) or \(SL(2,\mathbb{R})\). Examples in the Sasakian and flat cases are well known and here we give explicitly such a structure on these Lie groups.
It is shown that a 3-dimensional contact metric manifold on which \(Q\phi=\phi Q\) is either Sasakian, flat or locally isometric to a left invariant metric on the Lie group \(SU(2)\) or \(SL(2,\mathbb{R})\). Examples in the Sasakian and flat cases are well known and here we give explicitly such a structure on these Lie groups.
MSC:
| 53C15 | General geometric structures on manifolds (almost complex, almost product structures, etc.) |
| 53C25 | Special Riemannian manifolds (Einstein, Sasakian, etc.) |
