Genus one fibered knots in lens spaces (Q1107168)

Let M be an orientable closed 3-manifold and K a tame knot in M. We say that K is a genus one fibered knot in M if K is a fibered knot whose fiber is a torus with one hole. We call it a GOF-knot for brevity. Then it was proved by Burde, Zieschang and González-Acuña that \(S^ 3\) \((=L(1,1))\) contains exactly two GOF-knots, those are the trefoil knot and the figure eight knot. In this paper we determine GOF-knots in some lens spaces. In fact we have the following results. Each of L(0,1), L(5,2) and L(19,3) contains exactly one GOF-knot. Each of L(1,1), L(2,1), L(3,1), L(5,1) and L(19,1) contains exactly two GOF-knots. L(4,1) contains exactly three GOF-knots. And each of L(19,2), L(19,4) and L(19,7) does not contain a GOF-knot.