Open Access
august 2010 Foliations and complemented framed structures
Constantin Călin
Bull. Belg. Math. Soc. Simon Stevin 17(3): 499-512 (august 2010). DOI: 10.36045/bbms/1284570735


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.


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Constantin Călin. "Foliations and complemented framed structures." Bull. Belg. Math. Soc. Simon Stevin 17 (3) 499 - 512, august 2010.


Published: august 2010
First available in Project Euclid: 15 September 2010

zbMATH: 1204.53023
MathSciNet: MR2731371
Digital Object Identifier: 10.36045/bbms/1284570735

Primary: 53C40 , 53C55
Secondary: 53C12 , 53C42

Rights: Copyright © 2010 The Belgian Mathematical Society

Vol.17 • No. 3 • august 2010
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