On the cohomology algebra of some classes of geometrically formal manifolds

被引:7
作者
Grosjean, J. -F. [1 ]
Nagy, P. -A. [2 ]
机构
[1] Univ H Poincare, Inst Elie Cartan, F-54506 Vandoeuvre Les Nancy, France
[2] Univ Auckland, Dept Math, Auckland, New Zealand
关键词
HARMONIC FORMS;
D O I
10.1112/plms/pdn047
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We investigate harmonic forms of geometrically formal metrics, which are defined as those having the exterior product of any two harmonic forms still harmonic. We prove that a formal Sasakian metric can exist only on a real cohomology sphere and that holomorphic forms of a formal Kahler metric are parallel with respect to the Levi-Civita connection. In the general Riemannian case a formal metric with maximal second Betti number is shown to be flat. Finally we prove that a 6-dimensional manifold with b(1) not equal 1, b(2) >= 2 and not having the real cohomology algebra of (3) x S(3) carries a symplectic structure as soon as it admits a formal metric.
引用
收藏
页码:607 / 630
页数:24
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