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Kählerian Manifold on the Product of Two Trans-Sasakian Manifolds

Year 2020, Volume: 13 Issue: 2, 135 - 143, 15.10.2020
https://doi.org/10.36890/iejg.756830

Abstract

It's shown that for some changes of metrics and structural tensors, the product of two Trans-Sasakian manifolds is a K\"{a}hlerian manifold. This gives a new positive answer and more generally to Blair-Oubi$\tilde{n}$a's open question (see [7] and [17]). Concrete examples are given.                                                                                                            .......................................................................                                                                     

References

  • [1] Alegre, P. and Carriazo, A.: Generalized Sasakian Space Forms and Conformal Changes of the Metric. Results Math. 59, 485-493 (2011).
  • [2] Beldjilali, G. and Belkhelfa, M.: Kählerian structures on generalized doublyD-homothetic Bi-warping. African Diaspora Journal of Mathematics, Vol. 21(2), 1-14 (2018).
  • [3] Beldjilali, G.: Structures and D-isometric warping. HSIG, 2(1), 21-29 (2020).
  • [4] Boyer, C.P., Galicki, K. and Matzeu, P.: On Eta-Einstein Sasakian Geometry. Comm.Math. Phys., 262, 177-208 (2006).
  • [5] Blair, D. E.: Riemannian Geometry of Contact and Symplectic Manifolds. Progress in Mathematics 203, Birhauser, Boston, (2002).
  • [6] Blair D. E.: D-homothetic warping and appolications to geometric structures and cosmology . African Diaspora Journal of Math. 14, 134-144 (2013).
  • [7] Blair, D. E. and Oubi~na, J. A.: Conformal and related changes of metric on the product of two almost contact metric manifolds. Publ. Math. 34, 199-207 (1990).
  • [8] Caprusi, M.: Some remarks on the product of two almost contact manifolds. An. tiin. Univ. Al. I. Cuza Iad Sec. I a Mat . 30, 75-79 (1984).
  • [9] De, U.C. and Tripathi, M. M.: Ricci Tensor in 3-dimensional Trans-Sasakian Manifolds. Kyungpook Math. J. 43, 247-255 (2003).
  • [10] Marrero, J. C.: The local structure of trans-Sasakian manifolds. Annali di Matematica Pura ed Applicata , 162(1), 77-86 (1992).
  • [11] Morimoto, A.: On normal almost contact metric structures. J. Math. Soc. Japan, vol. 15(4), 1963.
  • [12] Olszak, Z.: Normal almost contact manifolds of dimension three. Annales Polonici Mathematici 47(1), 41-50 (1986).
  • [13] Özdemir, N., Aktay, S. and Solgun, M.: On Generalized D-Conformal Deformations of Certain Almost Contact Metric Manifolds. Mathematics , 7, 168; doi:10.3390/math7020168. (2019).
  • [14] Özdemir, N., Aktay, S. and Solgun, M.: Almost Hermitian structures on the products of two almost contact metric manifolds. Differ Geom Dyn Syst. 18, 102-109 (2016).
  • [15] Oubi~na, J. A.: New classes of almost contact metric structures. Publ. Math. Debrecen, 32, 187-193 (1985).
  • [16] Sharfuddin, A. and Hussain, S. I.: Almost contact structures induced by a conformal trasformation. Pub. Inst. Math. 32(46), 155-159 (1982).
  • [17] Tanno, S.: The topology of contact Riemannian manifolds. Illinois J. Math. 12 , 700-717 (1968).
  • [18] Watanabe, Y.: Almost Hermitian and Kähler structures on product manifolds. Proc of the Thirteenth International Workshop on Diff. Geom., 13, 1-16 (2009).
  • [19] Yano, K. and Kon, M.: Structures on Manifolds. Series in Pure Math., 3, World Sci., 1984.
Year 2020, Volume: 13 Issue: 2, 135 - 143, 15.10.2020
https://doi.org/10.36890/iejg.756830

Abstract

References

  • [1] Alegre, P. and Carriazo, A.: Generalized Sasakian Space Forms and Conformal Changes of the Metric. Results Math. 59, 485-493 (2011).
  • [2] Beldjilali, G. and Belkhelfa, M.: Kählerian structures on generalized doublyD-homothetic Bi-warping. African Diaspora Journal of Mathematics, Vol. 21(2), 1-14 (2018).
  • [3] Beldjilali, G.: Structures and D-isometric warping. HSIG, 2(1), 21-29 (2020).
  • [4] Boyer, C.P., Galicki, K. and Matzeu, P.: On Eta-Einstein Sasakian Geometry. Comm.Math. Phys., 262, 177-208 (2006).
  • [5] Blair, D. E.: Riemannian Geometry of Contact and Symplectic Manifolds. Progress in Mathematics 203, Birhauser, Boston, (2002).
  • [6] Blair D. E.: D-homothetic warping and appolications to geometric structures and cosmology . African Diaspora Journal of Math. 14, 134-144 (2013).
  • [7] Blair, D. E. and Oubi~na, J. A.: Conformal and related changes of metric on the product of two almost contact metric manifolds. Publ. Math. 34, 199-207 (1990).
  • [8] Caprusi, M.: Some remarks on the product of two almost contact manifolds. An. tiin. Univ. Al. I. Cuza Iad Sec. I a Mat . 30, 75-79 (1984).
  • [9] De, U.C. and Tripathi, M. M.: Ricci Tensor in 3-dimensional Trans-Sasakian Manifolds. Kyungpook Math. J. 43, 247-255 (2003).
  • [10] Marrero, J. C.: The local structure of trans-Sasakian manifolds. Annali di Matematica Pura ed Applicata , 162(1), 77-86 (1992).
  • [11] Morimoto, A.: On normal almost contact metric structures. J. Math. Soc. Japan, vol. 15(4), 1963.
  • [12] Olszak, Z.: Normal almost contact manifolds of dimension three. Annales Polonici Mathematici 47(1), 41-50 (1986).
  • [13] Özdemir, N., Aktay, S. and Solgun, M.: On Generalized D-Conformal Deformations of Certain Almost Contact Metric Manifolds. Mathematics , 7, 168; doi:10.3390/math7020168. (2019).
  • [14] Özdemir, N., Aktay, S. and Solgun, M.: Almost Hermitian structures on the products of two almost contact metric manifolds. Differ Geom Dyn Syst. 18, 102-109 (2016).
  • [15] Oubi~na, J. A.: New classes of almost contact metric structures. Publ. Math. Debrecen, 32, 187-193 (1985).
  • [16] Sharfuddin, A. and Hussain, S. I.: Almost contact structures induced by a conformal trasformation. Pub. Inst. Math. 32(46), 155-159 (1982).
  • [17] Tanno, S.: The topology of contact Riemannian manifolds. Illinois J. Math. 12 , 700-717 (1968).
  • [18] Watanabe, Y.: Almost Hermitian and Kähler structures on product manifolds. Proc of the Thirteenth International Workshop on Diff. Geom., 13, 1-16 (2009).
  • [19] Yano, K. and Kon, M.: Structures on Manifolds. Series in Pure Math., 3, World Sci., 1984.
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Bouzir Habib

Beldjılalı Gherici 0000-0002-8933-1548

Publication Date October 15, 2020
Acceptance Date September 23, 2020
Published in Issue Year 2020 Volume: 13 Issue: 2

Cite

APA Habib, B., & Gherici, B. (2020). Kählerian Manifold on the Product of Two Trans-Sasakian Manifolds. International Electronic Journal of Geometry, 13(2), 135-143. https://doi.org/10.36890/iejg.756830
AMA Habib B, Gherici B. Kählerian Manifold on the Product of Two Trans-Sasakian Manifolds. Int. Electron. J. Geom. October 2020;13(2):135-143. doi:10.36890/iejg.756830
Chicago Habib, Bouzir, and Beldjılalı Gherici. “Kählerian Manifold on the Product of Two Trans-Sasakian Manifolds”. International Electronic Journal of Geometry 13, no. 2 (October 2020): 135-43. https://doi.org/10.36890/iejg.756830.
EndNote Habib B, Gherici B (October 1, 2020) Kählerian Manifold on the Product of Two Trans-Sasakian Manifolds. International Electronic Journal of Geometry 13 2 135–143.
IEEE B. Habib and B. Gherici, “Kählerian Manifold on the Product of Two Trans-Sasakian Manifolds”, Int. Electron. J. Geom., vol. 13, no. 2, pp. 135–143, 2020, doi: 10.36890/iejg.756830.
ISNAD Habib, Bouzir - Gherici, Beldjılalı. “Kählerian Manifold on the Product of Two Trans-Sasakian Manifolds”. International Electronic Journal of Geometry 13/2 (October 2020), 135-143. https://doi.org/10.36890/iejg.756830.
JAMA Habib B, Gherici B. Kählerian Manifold on the Product of Two Trans-Sasakian Manifolds. Int. Electron. J. Geom. 2020;13:135–143.
MLA Habib, Bouzir and Beldjılalı Gherici. “Kählerian Manifold on the Product of Two Trans-Sasakian Manifolds”. International Electronic Journal of Geometry, vol. 13, no. 2, 2020, pp. 135-43, doi:10.36890/iejg.756830.
Vancouver Habib B, Gherici B. Kählerian Manifold on the Product of Two Trans-Sasakian Manifolds. Int. Electron. J. Geom. 2020;13(2):135-43.