Abstract
On an odd dimensional manifold, we define a structure which generalizes several known structures on almost contact manifolds, namely Sasakian, trans-Sasakian, quasi-Sasakian, Kenmotsu and cosymplectic structures. This structure, hereinafter called a G.Q.S. manifold, is defined on an almost contact metric manifold and satisfies an additional condition (1.5). We then consider a codimension-one distribution on a G.Q.S. manifold. Necessary and sufficient conditions for the normality of the complemented framed structure on the distribution defined on a G.Q.S manifold are studied (Th. 3.2). The existence of the foliation on G.Q.S. manifolds and of bundle-like metrics are also proven. It is shown that under certain circumstances a new foliation arises and its properties are investigated. Some examples illustrating these results are given in the final part of this paper.
Citation
Constantin Călin. "Foliations and complemented framed structures." Bull. Belg. Math. Soc. Simon Stevin 17 (3) 499 - 512, august 2010. https://doi.org/10.36045/bbms/1284570735
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