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Screen Generic Lightlike Submanifolds of Indefinite Sasakian Manifolds

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Abstract

In this paper, we introduce the general notion of screen generic lightlike submanifolds of indefinite Sasakian manifolds. We study screen generic lightlike submnaifolds, contact totally umbilical screen generic lightlike submanifolds, and minimal screen generic lightlike submanifolds of indefinite Sasakian manifolds. Also, we provide some examples of screen generic lightlike submanifold and minimal screen generic lightlike submanifold of an indefinite Sasakian manifold.

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References

  1. Bejan, C.L., Duggal, K.L.: Global lightlike manifolds and harmonicity. Kodai Math. J. 28, 131–145 (2005)

    Article  MathSciNet  Google Scholar 

  2. Bejancu, A., Duggal, K.L.: Lightlike submanifolds of semi-Riemannian manifolds. Acta Appl. Math. 38, 197–215 (1995)

    Article  MathSciNet  Google Scholar 

  3. Blair, D.E.: Riemannian Geometry of Contact and Symplectic Manifolds. Birkhauser, Basel (2002)

    Book  Google Scholar 

  4. Chen, B.Y.: Differential geometry of real submanifolds in a Kähler manifold. Monatshefte Math. 91, 257–274 (1981)

    Article  MathSciNet  Google Scholar 

  5. Doğan, B., Şahin, B., Yaşar, E.: Screen generic lightlike submanifolds. Mediterr. J. Math. 16(4), 21 (2019)

    Article  MathSciNet  Google Scholar 

  6. Duggal, K.L., Bejancu, A.: CR-hypersurfaces of indefinite Kähler manifolds. Acta Appl. Math. 31, 171–190 (1993)

    Article  MathSciNet  Google Scholar 

  7. Duggal, K.L., Bejancu, A.: Lightlike Submanifolds of Semi-Riemannian Manifolds and its Applications. Kluwer Academic, Dordrecht (1996)

    Book  Google Scholar 

  8. Duggal, K.L., Jin, D.H.: Generic lightlike submanifolds an indefinite Sasakian manifold. Int. Electron. J. Geom. 5(1), 108–119 (2012)

    MathSciNet  MATH  Google Scholar 

  9. Duggal, K.L., Jin, D.H.: Totally umbilical lightlike submanifolds. Kodai Math J. 26, 49–68 (2003)

    Article  MathSciNet  Google Scholar 

  10. Duggal, K.L., Şahin, B.: Screen Cauchy Riemann lightlike submanifolds. Acta Math. Hungar. 106(1–2), 137–165 (2005)

    Article  MathSciNet  Google Scholar 

  11. Duggal, K.L., Şahin, B.: Differential Geometry of Lightlike Submanifolds, Frontiers in Mathematics. Birkhäuser, Basel (2010)

    Book  Google Scholar 

  12. Duggal, K.L., Şahin, B.: Generalized Cauchy Riemann lightlike submanifolds. Acta Math. Hungar. 112(1–2), 107–130 (2006)

    Article  MathSciNet  Google Scholar 

  13. Erdogan, F.E., Perktaṣ, S.Y., Güneṣ, R.: Half-lightlike submanifolds with degenerate and non-degenerate planar normal sections in pseudo-Euclidean spaces. Int. J. Geom. 7(1), 37–53 (2018)

    MathSciNet  MATH  Google Scholar 

  14. Erdogan, F.E., Yıldırım, C.: Lightlike submanifolds with planar normal section in semi Riemannian product manifolds. Int. Electron. J. Geom. 9(1), 70–77 (2016)

    Article  MathSciNet  Google Scholar 

  15. Gupta, R.S., Sharfuddin, A.: Screen transversal lightlike submanifolds of indefinite cosymplectic manifolds. Rend. Semin. Mat. Univ. Padova 124, 145–156 (2010)

    Article  MathSciNet  Google Scholar 

  16. Gupta, R.S., Upadhyay, A., Sharfuddin, A.: Slant lightlike submanifolds of indefinite cosymplectic manifolds. Mediterr. J. Math. 8(2), 215–227 (2011)

    Article  MathSciNet  Google Scholar 

  17. Jin, D.H., Lee, J.W.: Generic lightlike submanifolds of an indefinite Kähler manifold. Int. J. Pure Appl. Math. 101(4), 543–560 (2015)

    Google Scholar 

  18. Jin, D.H., Lee, J.W.: Generic lightlike submanifolds of an indefinite cosymplectic manifold. Math. Probl. Eng. 610986, 16 (2011)

    MathSciNet  MATH  Google Scholar 

  19. Kumar, S.: Geometry of warped product lightlike submanifolds of indefinite nearly Kaehler manifolds. J. Geom. 109(1), 18 (2018)

    Article  MathSciNet  Google Scholar 

  20. Poyraz, N.O., Yaşar, E.: Lightlike hypersurfaces of a golden semi-Riemannian manifold. Mediterr. J. Math. 14(5), 204 (2017)

    Article  MathSciNet  Google Scholar 

  21. Şahin, B.: Screen transversal lightlike submanifolds of Kähler manifolds. Chaos Solitons Fract. 38, 1439–1448 (2008)

    Article  Google Scholar 

  22. Şahin, B., Güneş, R.: Geodesic CR-lightlike submanifolds. Beiträge Algebra Geom. 42(2), 583–594 (2001)

    MathSciNet  MATH  Google Scholar 

  23. Upadhyay, A., Gupta, R.S., Sharfuddin, A.: Screen conformal lightlike hypersurfaces of an indefinite cosymplectic manifold. Georgian Math. J. 24(4), 609–620 (2017)

    Article  MathSciNet  Google Scholar 

  24. Yano, K., Kon, M.: Structures on Manifolds Series in Pure Mathematics, vol. 3. World Scientific, Singapore (1984)

    MATH  Google Scholar 

  25. Yano, K., Kon, M.: Generic submanifolds of Sasakian manifolds. Kodai Math. J. 3, 163–196 (1980)

    Article  MathSciNet  Google Scholar 

  26. Yıldırım, C., Erdoḡan, F.E.: Radical screen transversal lightlike submanifolds of semi-Riemannian product manifolds. Math. Sci. Appl. E-Notes 3(1), 75–85 (2015)

    MathSciNet  MATH  Google Scholar 

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Acknowledgements

The author would like to thank reviewers for valuable suggestions to improve the article.

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  1. University School of Basic and Applied Sciences, Guru Gobind Singh Indraprastha University, Sector-16C, Dwarka, New Delhi, 110078, India

    Ram Shankar Gupta

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  1. Ram Shankar Gupta
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Correspondence to Ram Shankar Gupta.

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This work is supported by award of grant under FRGS for the year 2019–20, F.No. GGSIPU/DRC/FRGS/2019/1553/5.

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Gupta, R.S. Screen Generic Lightlike Submanifolds of Indefinite Sasakian Manifolds. Mediterr. J. Math. 17, 141 (2020). https://doi.org/10.1007/s00009-020-01590-8

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