Results in Mathematics

, 74:15 | Cite as

Almost Para-Hermitian and Almost Paracontact Metric Structures Induced by Natural Riemann Extensions

  • Cornelia-Livia Bejan
  • Galia NakovaEmail author


The context of our work is a manifold \((M,\nabla )\) with a symmetric linear connection \(\nabla \) which induces on the cotangent bundle \(T^*M\) of M a semi-Riemannian metric \({\overline{g}}\) with a neutral signature. The metric \({\overline{g}}\) is called natural Riemann extension and it is a generalization (due to Sekizawa and Kowalski) of the Riemann extension, introduced by Patterson and Walker (Q J Math Oxford Ser 2(3):19–28, 1952). We construct almost para-Hermitian structures on \((T^*M,{\overline{g}})\) which are almost para-Kähler or para-Kähler and prove that the defined almost para-complex structures are harmonic. On certain hypersurfaces of \(T^*M\) we construct almost paracontact metric structures, induced by the obtained almost para-Hermitian structures. We determine the classes of the corresponding almost paracontact metric manifolds according to the classification given by Zamkovoy and Nakova (J Geom 109(1):18, 2018. We obtain a necessary and sufficient condition for the considered manifolds to be paracontact metric, K-paracontact metric or para-Sasakian.


Natural Riemann extension almost para-Hermitian structures almost paracontact manifolds harmonicity 

Mathematics Subject Classification




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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Mathematics”Gh. Asachi” Technical University of IasiIasiRomania
  2. 2.Department of Algebra and Geometry, Faculty of Mathematics and Informatics“St. Cyril and St. Methodius” University of Veliko TarnovoVeliko TarnovoBulgaria

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