Let M be a positive quaternionic Kahler manifold of dimension 4m. We already showed that if the symmetry rank is greater than or equal to [m/2] ＋ 2 and the fourth Betti number b4 is equal to one, then M is isometric ...Let M be a positive quaternionic Kahler manifold of dimension 4m. We already showed that if the symmetry rank is greater than or equal to [m/2] ＋ 2 and the fourth Betti number b4 is equal to one, then M is isometric to HPm. The goal of this paper is to report that we can improve the lower bound of the symmetry rank by one for higher even-dimensional positive quaternionic Kahler manifolds. Namely, it is shown in this paper that if the symmetry rank of M with b4（M） = 1 is greater than or equal to m/2 ＋ 1 for m ≥ 10, then M is isometric to HPm. One of the main strategies of this paper is to apply a more delicate argument of Frankel type to positive quaternionic Kahler manifolds with certain symmetry rank.展开更多
基金Supported by Grant No. R01-2006-000-10152-0 from the Basic Research Program of the Korea Science Engineering Foundationthe SRC Program of KOSEF and the BK21 Program of KAIST
文摘Let M be a positive quaternionic Kahler manifold of dimension 4m. We already showed that if the symmetry rank is greater than or equal to [m/2] ＋ 2 and the fourth Betti number b4 is equal to one, then M is isometric to HPm. The goal of this paper is to report that we can improve the lower bound of the symmetry rank by one for higher even-dimensional positive quaternionic Kahler manifolds. Namely, it is shown in this paper that if the symmetry rank of M with b4（M） = 1 is greater than or equal to m/2 ＋ 1 for m ≥ 10, then M is isometric to HPm. One of the main strategies of this paper is to apply a more delicate argument of Frankel type to positive quaternionic Kahler manifolds with certain symmetry rank.
