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Extremities Involving B. Y. Chen’s Invariants for Real Hypersurfaces in Complex Quadric

Year 2018, Volume: 11 Issue: 2, 34 - 46, 30.11.2018
https://doi.org/10.36890/iejg.545120

Abstract

References

  • [1] Arslan, K., Ezentas, R., Mihai, I., Özgür, C., Certain inequalities for submanifolds in (k, µ)--contact space forms. Bull. Aust. Math. Soc., 64 (2001), no. 2, 201-212.
  • [2] Bansal, P., Shahid, M. H., Non-existence of Hopf real hypersurfaces in complex quadric with recurrent Ricci tensor, Appl. Appl. Math. 13 (2018), in press.
  • [3] Bansal, P., Shahid, M. H., Optimization approach for bounds involving generalised normalised δ-Casorati curvatures, Advances in Intelligent Systems and Computing, 741 (2018), 227-237.
  • [4] Bansal, P., Shahid, M. H., Bounds of generalized normalized δ-Casorati curvatures for real hypersurfaces in the complex quadric, Arab. J. Math., (2018), in press.
  • [5] Berndt, J., Suh, Y. J., Real hypersurfaces with isometric Reeb flow in complex quadrics, Internat. J. Math., 24 (2013), 1350050, 18pp.
  • [6] Blair, D. E., Contact manifolds in Riemannian Geometry. Lecture Notes in Math, 509, Springer-Verlag, Berlin, (1976).
  • [7] Chen, B. Y., Differential Geometry ofWarped Product Manifolds and Submanifolds,World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2017.
  • [8] Chen, B. Y., Geometry of warped products as Riemannian submanifolds and related problem, Soochow J. Math., 28 (2002), 125-157.
  • [9] Chen, B. Y., Some pinching and classification theorems for minimal submanifolds, Arch. Math. (Basel), 60 (1993), 568-578.
  • [10] Chen, B. Y., A Riemannian invariant and its applications to submanifold theory, Result. Math., 27 (1995), 17-26.
  • [11] Chen, B. Y., Ideal Lagrangian immersions in complex space forms, Math. Proc. Cambridge Philos. Soc., 128 (2000), 511-533.
  • [12] Chern, S. S., Minimal Submanifolds in a Riemannian Manifold, University of Kansas Press, (1968).
  • [13] Cioroboiu, D., Chen, B. Y., inequalities for semi-slant submanifolds in Sasakian space forms, Int. J. Math. Math. Sci, 27 (2003), 1731-1738.
  • [14] Hayden, H. A., Subspaces of a space with torsion, Proc. Lond. Math. Soc., 34 (1932), 27-50.
  • [15] Mihai, A., Özgür, C., Chen inequalities for submanifolds of real space forms with a semi-symmetric metric connection, Taiwanese J. Math., 14 (2010), 1465-1477.
  • [16] Reckziegel, H., On the geometry of the complex quadric, in :Geometry and Topology of Submanifolds VIII (Brussels/Nordfjordeid 1995), World Sci. Publ., River Edge, NJ, (1995), 302-315.
  • [17] Suh, Y. J., Real hypersurfaces in the complex quadric with parallel Ricci tensor, Advances in Mathematics, 281 (2015), 886-905.
  • [18] Suh, Y. J., Real hypersurfaces in the complex quadric with Reeb parallel shape operator, Internat. J. Math., 25 (2014), 1450059, 17pp.
  • [19] Suh, Y. J., Psuedo-Einstein real hypersurfaces in the complex quadric, Math. Nachr., 290 (2017), no. 11-12, 1884-1904.
  • [20] Yano, K., On semi-symmetric metric connection, Rev. Roumaine Math. Pures Appl., 15 (1970), 1579-1586.
Year 2018, Volume: 11 Issue: 2, 34 - 46, 30.11.2018
https://doi.org/10.36890/iejg.545120

Abstract

References

  • [1] Arslan, K., Ezentas, R., Mihai, I., Özgür, C., Certain inequalities for submanifolds in (k, µ)--contact space forms. Bull. Aust. Math. Soc., 64 (2001), no. 2, 201-212.
  • [2] Bansal, P., Shahid, M. H., Non-existence of Hopf real hypersurfaces in complex quadric with recurrent Ricci tensor, Appl. Appl. Math. 13 (2018), in press.
  • [3] Bansal, P., Shahid, M. H., Optimization approach for bounds involving generalised normalised δ-Casorati curvatures, Advances in Intelligent Systems and Computing, 741 (2018), 227-237.
  • [4] Bansal, P., Shahid, M. H., Bounds of generalized normalized δ-Casorati curvatures for real hypersurfaces in the complex quadric, Arab. J. Math., (2018), in press.
  • [5] Berndt, J., Suh, Y. J., Real hypersurfaces with isometric Reeb flow in complex quadrics, Internat. J. Math., 24 (2013), 1350050, 18pp.
  • [6] Blair, D. E., Contact manifolds in Riemannian Geometry. Lecture Notes in Math, 509, Springer-Verlag, Berlin, (1976).
  • [7] Chen, B. Y., Differential Geometry ofWarped Product Manifolds and Submanifolds,World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2017.
  • [8] Chen, B. Y., Geometry of warped products as Riemannian submanifolds and related problem, Soochow J. Math., 28 (2002), 125-157.
  • [9] Chen, B. Y., Some pinching and classification theorems for minimal submanifolds, Arch. Math. (Basel), 60 (1993), 568-578.
  • [10] Chen, B. Y., A Riemannian invariant and its applications to submanifold theory, Result. Math., 27 (1995), 17-26.
  • [11] Chen, B. Y., Ideal Lagrangian immersions in complex space forms, Math. Proc. Cambridge Philos. Soc., 128 (2000), 511-533.
  • [12] Chern, S. S., Minimal Submanifolds in a Riemannian Manifold, University of Kansas Press, (1968).
  • [13] Cioroboiu, D., Chen, B. Y., inequalities for semi-slant submanifolds in Sasakian space forms, Int. J. Math. Math. Sci, 27 (2003), 1731-1738.
  • [14] Hayden, H. A., Subspaces of a space with torsion, Proc. Lond. Math. Soc., 34 (1932), 27-50.
  • [15] Mihai, A., Özgür, C., Chen inequalities for submanifolds of real space forms with a semi-symmetric metric connection, Taiwanese J. Math., 14 (2010), 1465-1477.
  • [16] Reckziegel, H., On the geometry of the complex quadric, in :Geometry and Topology of Submanifolds VIII (Brussels/Nordfjordeid 1995), World Sci. Publ., River Edge, NJ, (1995), 302-315.
  • [17] Suh, Y. J., Real hypersurfaces in the complex quadric with parallel Ricci tensor, Advances in Mathematics, 281 (2015), 886-905.
  • [18] Suh, Y. J., Real hypersurfaces in the complex quadric with Reeb parallel shape operator, Internat. J. Math., 25 (2014), 1450059, 17pp.
  • [19] Suh, Y. J., Psuedo-Einstein real hypersurfaces in the complex quadric, Math. Nachr., 290 (2017), no. 11-12, 1884-1904.
  • [20] Yano, K., On semi-symmetric metric connection, Rev. Roumaine Math. Pures Appl., 15 (1970), 1579-1586.
There are 20 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Pooja Bansal This is me

Siraj Uddin

Mohammad Hasan Shahid

Publication Date November 30, 2018
Published in Issue Year 2018 Volume: 11 Issue: 2

Cite

APA Bansal, P., Uddin, S., & Shahid, M. H. (2018). Extremities Involving B. Y. Chen’s Invariants for Real Hypersurfaces in Complex Quadric. International Electronic Journal of Geometry, 11(2), 34-46. https://doi.org/10.36890/iejg.545120
AMA Bansal P, Uddin S, Shahid MH. Extremities Involving B. Y. Chen’s Invariants for Real Hypersurfaces in Complex Quadric. Int. Electron. J. Geom. November 2018;11(2):34-46. doi:10.36890/iejg.545120
Chicago Bansal, Pooja, Siraj Uddin, and Mohammad Hasan Shahid. “Extremities Involving B. Y. Chen’s Invariants for Real Hypersurfaces in Complex Quadric”. International Electronic Journal of Geometry 11, no. 2 (November 2018): 34-46. https://doi.org/10.36890/iejg.545120.
EndNote Bansal P, Uddin S, Shahid MH (November 1, 2018) Extremities Involving B. Y. Chen’s Invariants for Real Hypersurfaces in Complex Quadric. International Electronic Journal of Geometry 11 2 34–46.
IEEE P. Bansal, S. Uddin, and M. H. Shahid, “Extremities Involving B. Y. Chen’s Invariants for Real Hypersurfaces in Complex Quadric”, Int. Electron. J. Geom., vol. 11, no. 2, pp. 34–46, 2018, doi: 10.36890/iejg.545120.
ISNAD Bansal, Pooja et al. “Extremities Involving B. Y. Chen’s Invariants for Real Hypersurfaces in Complex Quadric”. International Electronic Journal of Geometry 11/2 (November 2018), 34-46. https://doi.org/10.36890/iejg.545120.
JAMA Bansal P, Uddin S, Shahid MH. Extremities Involving B. Y. Chen’s Invariants for Real Hypersurfaces in Complex Quadric. Int. Electron. J. Geom. 2018;11:34–46.
MLA Bansal, Pooja et al. “Extremities Involving B. Y. Chen’s Invariants for Real Hypersurfaces in Complex Quadric”. International Electronic Journal of Geometry, vol. 11, no. 2, 2018, pp. 34-46, doi:10.36890/iejg.545120.
Vancouver Bansal P, Uddin S, Shahid MH. Extremities Involving B. Y. Chen’s Invariants for Real Hypersurfaces in Complex Quadric. Int. Electron. J. Geom. 2018;11(2):34-46.