Research Article
BibTex RIS Cite

Structures on the Product of Two Almost Hermitian Almost Contact Manifolds

Year 2016, , 80 - 86, 30.10.2016
https://doi.org/10.36890/iejg.584602

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].

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.
Year 2016, , 80 - 86, 30.10.2016
https://doi.org/10.36890/iejg.584602

Abstract

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.
There are 15 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Gherici Beldjilali This is me

Mohamed Belkhelfa This is me

Publication Date October 30, 2016
Published in Issue Year 2016

Cite

APA Beldjilali, G., & Belkhelfa, M. (2016). Structures on the Product of Two Almost Hermitian Almost Contact Manifolds. International Electronic Journal of Geometry, 9(2), 80-86. https://doi.org/10.36890/iejg.584602
AMA Beldjilali G, Belkhelfa M. Structures on the Product of Two Almost Hermitian Almost Contact Manifolds. Int. Electron. J. Geom. October 2016;9(2):80-86. doi:10.36890/iejg.584602
Chicago Beldjilali, Gherici, and Mohamed Belkhelfa. “Structures on the Product of Two Almost Hermitian Almost Contact Manifolds”. International Electronic Journal of Geometry 9, no. 2 (October 2016): 80-86. https://doi.org/10.36890/iejg.584602.
EndNote Beldjilali G, Belkhelfa M (October 1, 2016) Structures on the Product of Two Almost Hermitian Almost Contact Manifolds. International Electronic Journal of Geometry 9 2 80–86.
IEEE G. Beldjilali and M. Belkhelfa, “Structures on the Product of Two Almost Hermitian Almost Contact Manifolds”, Int. Electron. J. Geom., vol. 9, no. 2, pp. 80–86, 2016, doi: 10.36890/iejg.584602.
ISNAD Beldjilali, Gherici - Belkhelfa, Mohamed. “Structures on the Product of Two Almost Hermitian Almost Contact Manifolds”. International Electronic Journal of Geometry 9/2 (October 2016), 80-86. https://doi.org/10.36890/iejg.584602.
JAMA Beldjilali G, Belkhelfa M. Structures on the Product of Two Almost Hermitian Almost Contact Manifolds. Int. Electron. J. Geom. 2016;9:80–86.
MLA Beldjilali, Gherici and Mohamed Belkhelfa. “Structures on the Product of Two Almost Hermitian Almost Contact Manifolds”. International Electronic Journal of Geometry, vol. 9, no. 2, 2016, pp. 80-86, doi:10.36890/iejg.584602.
Vancouver Beldjilali G, Belkhelfa M. Structures on the Product of Two Almost Hermitian Almost Contact Manifolds. Int. Electron. J. Geom. 2016;9(2):80-6.

Cited By

Some flatness conditions on normal metric contact pairs
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
https://doi.org/10.31801/cfsuasmas.546701