arXiv subjects
Publications and source records attributed to Cornelia-Livia Bejan.
Corresponding to weak almost contact metric structures (defined recently by Rovenski and Wolak), we introduce and study here weak almost contact structures with B-metric, which generalize the classical almost contact structures with Norden metric (B-metric). Several geometric properties are obtained, some special classes are investigated and a lot of examples are constructed throughout this work.
In this paper we construct and study almost paracontact metric structures $(φ,ξ,η,g)$ on a 3-dimensional Walker manifold $(M,g)$ with respect to a local basis only by the coordinate functions of a unit space-like vector field $ξ$, globally defined on $M$ and a function $f$ on $M$, characterizing the Lorentzian metric $g$. Necessary and sufficient conditions are obtained for $M$, endowed with these structures, to fall in one of the following classes of 3-dimensional almost paracontact metric manifolds according to the classification given by S. Zamkovoy and G. Nakova: paracontact metric, normal, almost $α$-paracosymplectic, almost paracosymplectic, paracosymplectic and $\mathbb{G}_{12}$-manifolds. Also, classes to which the studied manifolds do not belong are found. Special attention is paid to an $η$-Einstein manifold among the considered manifolds and its $ξ$-sectional, $φ$-sectional and scalar curvature are investigated. Examples of the examined manifolds are given.
In this paper we consider 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 (made by M. Sekizawa and O. Kowalski) of the Riemann extension, introduced by E. K. Patterson and A. G. Walker (1952). We construct two 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 S. Zamkovoy and G. Nakova (2018). We obtain a necessary and sufficient condition the considered manifolds to be paracontact metric, K-paracontact metric or para-Sasakian.