Nullity conditions in paracontact geometry

By B. C. Montano, I. Erken, C. Murathan. 2012

99 citations recorded by the source corpus.

Abstract The paper is a complete study of paracontact metric manifolds for which the Reeb vector field of the underlying contact structure satisfies a nullity condition (the condition (1.2), for some real numbers κ ˜ and μ ˜ ). This class of pseudo-Riemannian manifolds, which includes para-Sasakian manifolds, was recently defined in Cappelletti Montano (2010) [13] . In this paper we show in fact that there is a kind of duality between those manifolds and contact metric ( κ , μ ) -spaces. In particular, we prove that, under some natural assumption, any such paracontact metric manifold admits a compatible contact metric ( κ , μ ) -structure (eventually Sasakian). Moreover, we prove that the nullity condition is invariant under D -homothetic deformations and determines the whole curvature tensor field completely. Finally non-trivial examples in any dimension are presented and the many differences with the contact metric case, due to the non-positive definiteness of the metric, are discussed.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/65d80adcc1cada4892319ed16c7a21f7caa195d5

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In Applied Mathematics

1. D. Perrone
2. Giovanni Calvaruso

Citations in the corpus

• Geometry of $H$-paracontact metric manifolds (2013, background): “It is interesting to investigate non-paraSasakian paracontact (κ, μ)-spaces with κ = −1 [11], also in order to decide whether their Reeb vector field defines a harmonic map into the unit tangent sphere bundle.”