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Contact CR-Warped Product Submanifolds of Nearly Lorentzian Para-Sasakian Manifolds

Year 2017, Volume: 7, 40 - 47, 19.12.2017

Abstract

In the present paper we have investigated CR-submanifold of a nearly Lorentzian para-Sasakian manifolds, generalizing sharp inequality namely $||h||^{2}\geq \frac{2}{9} s +2s ||\nabla \ln f||^{2}$, for contact CR-warped products of nearly Lorentzian para-Sasakian manifolds. It is also proved that the derive inequalities for contact CR-warped products either in any contact metric manifold. The equality case is also handled.

References

  • Agrawal, N. K., Rahman, S., Characterization of canonical semi symmetric semi-metric connection on transversal hypersurfaces of Lorentzian para Sasakian manifolds, International Journal of Emerging Technology and Advanced Engineering, 6(10)(2016), 153–159.
  • Ahmad, A., Rahman, S., A note on transversal hypersurfaces of Lorentzian para-Sasakian manifolds with a semi-symmetric non-metric connection, Journal of Tensor Society, 8(2014), 53–63.
  • Alegre, P., CR-submanifolds of Lorentzian manifolds, Int. Elect. J. Geom. 2(2009), 95–103.
  • Arslan, K., Ezentas, R., Mihai, I., Murathan, C., Contact CR-warped product submanifolds in Kenmotsu space forms, J. Korean Math. Soc., 42(2005), 1101–1110.
  • Bishop, R. L., O’Neill, B., Manifolds of negative curvature, Trans. Amer. Math. Soc., 145(1969), 1–49.
  • Bonanzinga, V., Matsumoto, K., Warped product CR-submanifolds in locally conformal Kaehler manifolds, Periodica Math. Hungar., 48(2004), 207–221.
  • Chen, B. Y., Geometry of warped product CR-submanifolds in Kaehler manifolds I, Monatsh. Math., 133(2001), 177–195.
  • Chen, B. Y., Geometry of warped product CR-submanifolds in Kaehler manifolds II, Monatsh. Math., 134(2001), 103–119.
  • De, U.C., Matsumoto, K., Shaikh, A. A., On Lorentzian para-Sasakian manifolds, Rendicontidel Seminario Matematico di Messina, Serie II, Supplemento al n. 3(1999), 149–158.
  • Hasegawa, I., Mihai, I., Contact CR-warped product submanifolds in Sasakian manifolds, Geom. Dedicata, 102(2003), 143–150.
  • Hiepko, S., Eine inner kennzeichungder verzerrten produkte, Math. Ann., 241(1979), 209–215.
  • Matsumoto, K., On Lorentzian para contact manifolds, Bull. of Yamagata Univ., Nat. Sci., 12(1989), 151–156.
  • Mihai, I., Contact CR-warped product submanifolds in Sasakian space forms, Geom.Dedicata, 109(2004), 165–173.
  • Mihai I., Rosca, R., On Lorentzian P-Sasakian Manifolds, Classical Analysis, World Scientific Publ., 1992, 155–169.
  • Rahman, S. Transversal hypersurfaces of a Lorentzian para-Sasakian manifold with a semi-symmetric metric connection, Journal of Qafqaz University- Mathematics and Computer Science, 1(2)(2013) 137–144.
  • Rahman, S.,Characterization of quarter symmetric non-metric connection on transversal hypersurfaces of Lorentzian para-Sasakian manifolds, Journal of Tensor Society, 8(2014), 65–75.
  • Rahman, S., Characterization of quarter symmetric semi metric connection on transversal hypersurfaces of Lorentzian para Sasakian manifolds, Journal of Qafqaz University- Mathematics and Computer Science 3(1)(2015), 09–17.
  • Rahman, S., Jun, J. B., Ahmad, A., On semi-invariant submanifolds of a nearly Lorentzian para-Sasakian manifold, Far East Journal of Mathematical Sciences, 96(6)(2015), 709–724.
Year 2017, Volume: 7, 40 - 47, 19.12.2017

Abstract

References

  • Agrawal, N. K., Rahman, S., Characterization of canonical semi symmetric semi-metric connection on transversal hypersurfaces of Lorentzian para Sasakian manifolds, International Journal of Emerging Technology and Advanced Engineering, 6(10)(2016), 153–159.
  • Ahmad, A., Rahman, S., A note on transversal hypersurfaces of Lorentzian para-Sasakian manifolds with a semi-symmetric non-metric connection, Journal of Tensor Society, 8(2014), 53–63.
  • Alegre, P., CR-submanifolds of Lorentzian manifolds, Int. Elect. J. Geom. 2(2009), 95–103.
  • Arslan, K., Ezentas, R., Mihai, I., Murathan, C., Contact CR-warped product submanifolds in Kenmotsu space forms, J. Korean Math. Soc., 42(2005), 1101–1110.
  • Bishop, R. L., O’Neill, B., Manifolds of negative curvature, Trans. Amer. Math. Soc., 145(1969), 1–49.
  • Bonanzinga, V., Matsumoto, K., Warped product CR-submanifolds in locally conformal Kaehler manifolds, Periodica Math. Hungar., 48(2004), 207–221.
  • Chen, B. Y., Geometry of warped product CR-submanifolds in Kaehler manifolds I, Monatsh. Math., 133(2001), 177–195.
  • Chen, B. Y., Geometry of warped product CR-submanifolds in Kaehler manifolds II, Monatsh. Math., 134(2001), 103–119.
  • De, U.C., Matsumoto, K., Shaikh, A. A., On Lorentzian para-Sasakian manifolds, Rendicontidel Seminario Matematico di Messina, Serie II, Supplemento al n. 3(1999), 149–158.
  • Hasegawa, I., Mihai, I., Contact CR-warped product submanifolds in Sasakian manifolds, Geom. Dedicata, 102(2003), 143–150.
  • Hiepko, S., Eine inner kennzeichungder verzerrten produkte, Math. Ann., 241(1979), 209–215.
  • Matsumoto, K., On Lorentzian para contact manifolds, Bull. of Yamagata Univ., Nat. Sci., 12(1989), 151–156.
  • Mihai, I., Contact CR-warped product submanifolds in Sasakian space forms, Geom.Dedicata, 109(2004), 165–173.
  • Mihai I., Rosca, R., On Lorentzian P-Sasakian Manifolds, Classical Analysis, World Scientific Publ., 1992, 155–169.
  • Rahman, S. Transversal hypersurfaces of a Lorentzian para-Sasakian manifold with a semi-symmetric metric connection, Journal of Qafqaz University- Mathematics and Computer Science, 1(2)(2013) 137–144.
  • Rahman, S.,Characterization of quarter symmetric non-metric connection on transversal hypersurfaces of Lorentzian para-Sasakian manifolds, Journal of Tensor Society, 8(2014), 65–75.
  • Rahman, S., Characterization of quarter symmetric semi metric connection on transversal hypersurfaces of Lorentzian para Sasakian manifolds, Journal of Qafqaz University- Mathematics and Computer Science 3(1)(2015), 09–17.
  • Rahman, S., Jun, J. B., Ahmad, A., On semi-invariant submanifolds of a nearly Lorentzian para-Sasakian manifold, Far East Journal of Mathematical Sciences, 96(6)(2015), 709–724.
There are 18 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

Shamsur Rahman

Publication Date December 19, 2017
Published in Issue Year 2017 Volume: 7

Cite

APA Rahman, S. (2017). Contact CR-Warped Product Submanifolds of Nearly Lorentzian Para-Sasakian Manifolds. Turkish Journal of Mathematics and Computer Science, 7, 40-47.
AMA Rahman S. Contact CR-Warped Product Submanifolds of Nearly Lorentzian Para-Sasakian Manifolds. TJMCS. December 2017;7:40-47.
Chicago Rahman, Shamsur. “Contact CR-Warped Product Submanifolds of Nearly Lorentzian Para-Sasakian Manifolds”. Turkish Journal of Mathematics and Computer Science 7, December (December 2017): 40-47.
EndNote Rahman S (December 1, 2017) Contact CR-Warped Product Submanifolds of Nearly Lorentzian Para-Sasakian Manifolds. Turkish Journal of Mathematics and Computer Science 7 40–47.
IEEE S. Rahman, “Contact CR-Warped Product Submanifolds of Nearly Lorentzian Para-Sasakian Manifolds”, TJMCS, vol. 7, pp. 40–47, 2017.
ISNAD Rahman, Shamsur. “Contact CR-Warped Product Submanifolds of Nearly Lorentzian Para-Sasakian Manifolds”. Turkish Journal of Mathematics and Computer Science 7 (December 2017), 40-47.
JAMA Rahman S. Contact CR-Warped Product Submanifolds of Nearly Lorentzian Para-Sasakian Manifolds. TJMCS. 2017;7:40–47.
MLA Rahman, Shamsur. “Contact CR-Warped Product Submanifolds of Nearly Lorentzian Para-Sasakian Manifolds”. Turkish Journal of Mathematics and Computer Science, vol. 7, 2017, pp. 40-47.
Vancouver Rahman S. Contact CR-Warped Product Submanifolds of Nearly Lorentzian Para-Sasakian Manifolds. TJMCS. 2017;7:40-7.