On N(k)-Contact Metric Manifolds

Abstract

The object of the present paper is to study a type of contact metric manifolds, called N (k)-contact metric manifolds admitting a non-null concircular and torse forming vector field. Among others it is shown that such a manifold is either locally isometric to the Riemannian product E n+1 (0) × S n (4) or a Sasakian manifold. Also it is shown that such a contact metric manifold can be expressed as a warped product I×ep * M , where ( * M , * g ) is a 2n-dimensional manifold. RESUMENEl objetivo del presente artículo es estudiar un tipo de variedades métricas de contacto, llamadas N (k)-variedades métricas de contacto admitiendo un campo de vectores concircular y forma torse. Es demostrado también que tales variedades son o localmente isométricas a productos Riemannianos E n+1 (0) × S n (4) o una variedade Sasakian. Es demostrado que tales variedades métricas de contacto pueden ser expresadas como un producto deformado I×ep * M , donde ( * M , * g ) es una variedad 2n-dimensional. 12, 1 (2010)

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“…Then putting , (13)  X = U = e i in (20) and taking summation over i, 1≤ i ≤ n, and using (15), (10), (8) and (2), we get…”

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