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On almost cosymplectic manifolds of pointwise constant phi - sectional curvature

Daco P.

Prace Naukowe Instytutu Matematyki Politechniki Wrocławskiej. Konferencje

2003

Vol. 25, nr 4

7-13

The constancy of the phi-sectional curvature is one of the most natural curvature conditions applied to almost contact metric manifolds. However, almost cosymplectic manifolds satisfying this condition are not classified yet, even locally. In the present paper we prove the following partial result. Let M be an almost cosymplectic manifold of dimension greater-than or equal to - 5 and 1 its canonical foliation with almost Kahlerian leaves. If M is of pointwise constant phi - sectional curvature and any leaf M element of Fis of pointwise constant holomorphic sectional curvature, then M is locally a product of an almost Kahlerian manifold of pointwise constant holomorphic sectional curvature and an open interval. Examples of such manifolds are also discussed.