Some Results on Almost Contact Manifolds with B-Metric

Year 2025, Volume: 6 Issue: 1, 81 - 92, 31.01.2025

Nilüfer Özdemir , Elanur Eren

Abstract

In this work, almost contact B-metric manifolds and almost complex manifolds with Norden metric are considered. Almost complex manifolds with a Norden metric are obtained by the product of almost contact B-metric manifolds with R, where almost complex structure and metric on the product manifold depend on two functions of R. The relations between two classes of almost contact manifolds with B-metric (the classes F_4 and F_5 ) and classes of almost complex manifolds with a Norden metric are investigated.

Keywords

Almost complex manifold with a Norden metric, almost contact manifold, almost contact manifold with B-metric

References

• Blaga A.M., η -Ricci solitons on para-Kenmotsu manifolds, Balkan Journal of Geometry and Its Applications, 20(1), 1-13, 2015.
• Chinea D., Gonzalez C., A classification of almost contact metric manifolds, Annali di Matematica Pura ed Applicata, 156, 15-36, 1990.
• Cho J.T., Kimura M., Ricci solitons and real hypersurfaces in a complex space form, Tohoku Mathematical Journal, 61(2), 205-212, 2009.
• Fernandez M., Gray A., Riemannian manifolds with structure group G2 , Annali di Matematica Pura ed Applicata, 132, 19-45, 1982.
• Gadea P.M., Masque J.M., Classification of almost para-Hermitian manifolds, Rendiconti di Matematica, 7(11), 377-396, 1991.
• Ganchev G.T., Borisov A.V., Note on the almost complex manifolds with a Norden metric, Comptes Rendus de L’Academie Bulgare des Sciences, 39(5), 31-34, 1986.
• Ganchev G.T., Mihova V., Gribachev K., Almost contact manifolds with B-metric, Mathematica Balkanica, 7, 261-167, 1993.
• Gray A., Hervella L.M., The sixteen classes of almost Hermitian manifolds and their linear invariants, Annali di Matematica Pura ed Applicata, 123, 35-58, 1980.
• Ivanov S., Manev H., Manev M., Sasaki-like almost contact complex Riemannian manifolds, Journal of Geometry and Physics, 107, 136-148, 2016.
• Manev M., On the Conformal Geometry of Almost Contact Manifolds with B-metric, Ph. D. Thesis, University of Plovdiv, Bulgaria, 1998.
• Manev M., Staikova M., On almost paracontact Riemannian manifolds of type (n,n), Journal of Geometry, 72, 108-114, 2001.
• Manev M., Ricci-like solitons on almost contact B-metric manifolds, Journal of Geometry and Physics, 154, 103734, 2020.
• Oubina J.A., A classification for almost contact structure, Preprint, 1985.
• Özdemir N., Erdo˘gan N., Some relations between almost paracontact metric manifolds and almost para-Hermitian manifolds, Turkish Journal of Mathematics, 46, 1459-1477, 2022.
• Özdemir N., Aktay S¸., Solgun M., Almost Hermitian structures from almost contact metric manifolds and their curvature properties, Konuralp Journal of Mathematics, 12(1), 5-12, 2024.
• Özdemir N., Aktay S¸., Solgun M., Some results on normal almost contact manifolds with B-metric, Kragujevac Journal of Mathematics, 50(4), 597-611, 2026.
• Patra D.S., Ricci solitons and paracontact geometry, Mediterranean Journal of Mathematics, 16, 137, 2019.
• Patra D.S., Rovenski V., Almost η -Ricci solitons on Kenmotsu manifolds, European Journal of Mathematics, 7, 1753-1766, 2021.
• Solgun M., On constructing almost complex Norden metric structures, AIMS Mathematics, 7(10), 17942-17953, 2022.
• Solgun M., Karababa Y., A natural way to construct an almost complex B-metric structure, Mathematical Methods in the Applied Sciences, 44(9), 7607-7613, 2021.
• Zamkovoy S., Nakova G., The decomposition of almost paracontact metric manifolds in eleven classes revisited, Journal of Geometry, 109(1), 18, 2018.