Summary
We consider a genaralization of contact metric manifolds given by assignment of 1-formsη1, . . . ,ηsand a compatible metric gon a manifold. With some integrability conditions they are called almost<span style='font-size:10.0pt;font-family:"Monotype Corsiva"; mso-bidi-font-family:"Monotype Corsiva"'>S-manifolds. We give a sufficient condition regarding the curvature of an almost<span style='font-size:10.0pt;font-family:"Monotype Corsiva";mso-bidi-font-family: "Monotype Corsiva"'>S-manifold to be locally isometric to a product of a Euclidean space and a sphere.
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Di Terlizzi, L. On the curvature of a generalization of contact metric manifolds. Acta Math Hung 110, 225–239 (2006). https://doi.org/10.1007/s10474-006-0018-8
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DOI: https://doi.org/10.1007/s10474-006-0018-8