Nullity conditions in paracontact geometry

Cappelletti Montano B., Erken I. K., Murathan C.

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, cilt.30, sa.6, ss.665-693, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 30 Sayı: 6
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1016/j.difgeo.2012.09.006
  • Dergi Adı: DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.665-693
  • Anahtar Kelimeler: Paracontact metric manifold, Para-Sasakian, Contact metric manifold, (kappa, mu)-manifold, Legendre foliation, CONTACT METRIC (KAPPA, MANIFOLDS
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

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 (kappa) over bar and (mu) over bar). 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 (kappa, mu)-spaces. In particular, we prove that, under some natural assumption, any such paracontact metric manifold admits a compatible contact metric (kappa, mu)-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. (C) 2012 Elsevier B.V. All rights reserved.