Structures on the Product of Two Almost Hermitian Almost Contact Manifolds

Year 2016, , 80 - 86, 30.10.2016

Gherici Beldjilali Mohamed Belkhelfa

https://doi.org/10.36890/iejg.584602

Cited By: 1

Abstract

The purpose of this paper is to define some classes of almost contact metric 3-structures manifolds

and almost quaternionic metric with an almost Hermitian almost contact metric structure. Next,

we construct an almost quaternionic Hermitian structure on the product of two almost Hermitian

almost contact metric structures. This gives a new positive answer to a question raised by T.

Tshikuna-Matamba [7].

Keywords

Almost Hermitian almost contact structure, almost contact metric manifolds with 3-structures, hyperkählerian structure

References

• [1] Blair, D. E., Riemannian Geometry of Contact and Symplectic Manifolds. Progress in Mathematics Vol. 203, Birhauser, Boston,2002. bibitemBGM Boyer, C. P., Galicki, K. and Mann, B. M., Quaternionic reduction and Einstein manifolds. Comm. Anal. Geom. 1(2), (1993) pp.229–279 .
• [2] Calabi, E., Métriques kählériennes et fibrés holomorphes. Ann. Scient. Ec. Norm.Sup. 12(1979), pp. 269-294.
• [3] Caprusi, M., Some remarks on the product of two almost contact manifolds. Al. I. Cuza, XXX, (1984) pp. 75–79 .
• [4] Ishihara, S. and Konishi, M., Complex almost contact manifolds. Kodai Math. J. 3, (1980) pp.385–396.
• [5] Kuo, Y., On almost contact 3-structures. Tohoku Math. J. (2) 22 (1970), 325–332.
• [6] Oubi~na, J. A., A classification for almost contact structures. manuscript (1985).
• [7] Satoh, H., Almost Hermitian structures on the tangent bundle. Procceedings of The Eleventh International Workshop on Differential.Geometry, Kyungpook Nat. Univ., Taegu, 11, (2007) pp.105–118 .
• [8] Sharauddin, A. and Husain, S. I., Almost contact structures induced by a confotmal transformation. Pub. Inst. Math. 32(46), (1982), pp. 155-159.
• [9] Tahara, M. and Watanabe, Y., Natural almost Hermitian, Hermitian and Kähler metrics on the tangent bundles. Math. J. Toyama Univ. 20(1997), pp. 149–160.
• [10] Tshikuna-Matamba, T., Quelques classes des variétés métriques à 3- structures presque de contact. Ann. Univ. Craiova, Math. Comp. Sci. Ser. 31(1) (2004), pp. 94-101.
• [11] Tshikuna-Matamba, T., Induced structures on the product of Riemannian manifolds. Int. Electron. J. Geo. Vol 4, (2011),pp. 15-25.
• [12] Watson, B., Riemannian submersions and non-linear gauge field equations of general relativity, in Global Analysis-Analysis in Manifolds, (T.M. Rassias ed.) Teubner-Texte Math, Vol. 57, Teubner, Leipzig, (1983), 324-349.
• [13] Watanabe, Y., Almost Hermitian and Kähler structures on product manifolds. Proc. of the Thirteenth International Workshop on Diff. Geom. 13, (2009) 1-16.
• [14] Watanabe, Y. and Hiroshi M., From Sasakian 3-structures to quaternionic geometry. Archivum Mathematicum, Vol. 34 (1998), No. 3, 379-386.
• [15] Yano, K. and Kon, M., Structures on Manifolds. Series in Pure Math., Vol 3, World Sci.,1984.