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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.

Details

Primary Language English
Journal Section Research Article
Authors

Pooja BANSAL This is me


Siraj UDDİN>


Mohammad Hasan SHAHİD>

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

Cite

Bibtex @research article { iejg545120, journal = {International Electronic Journal of Geometry}, eissn = {1307-5624}, address = {}, publisher = {Kazım İLARSLAN}, year = {2018}, volume = {11}, number = {2}, pages = {34 - 46}, doi = {10.36890/iejg.545120}, title = {Extremities Involving B. Y. Chen’s Invariants for Real Hypersurfaces in Complex Quadric}, key = {cite}, author = {Bansal, Pooja and Uddin, Siraj and Shahid, Mohammad Hasan} }
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 . DOI: 10.36890/iejg.545120
MLA Bansal, P. , Uddin, S. , Shahid, M. H. "Extremities Involving B. Y. Chen’s Invariants for Real Hypersurfaces in Complex Quadric" . International Electronic Journal of Geometry 11 (2018 ): 34-46 <https://dergipark.org.tr/en/pub/iejg/issue/44175/545120>
Chicago Bansal, P. , Uddin, S. , Shahid, M. H. "Extremities Involving B. Y. Chen’s Invariants for Real Hypersurfaces in Complex Quadric". International Electronic Journal of Geometry 11 (2018 ): 34-46
RIS TY - JOUR T1 - Extremities Involving B. Y. Chen’s Invariants for Real Hypersurfaces in Complex Quadric AU - PoojaBansal, SirajUddin, Mohammad HasanShahid Y1 - 2018 PY - 2018 N1 - doi: 10.36890/iejg.545120 DO - 10.36890/iejg.545120 T2 - International Electronic Journal of Geometry JF - Journal JO - JOR SP - 34 EP - 46 VL - 11 IS - 2 SN - -1307-5624 M3 - doi: 10.36890/iejg.545120 UR - https://doi.org/10.36890/iejg.545120 Y2 - 2022 ER -
EndNote %0 International Electronic Journal of Geometry Extremities Involving B. Y. Chen’s Invariants for Real Hypersurfaces in Complex Quadric %A Pooja Bansal , Siraj Uddin , Mohammad Hasan Shahid %T Extremities Involving B. Y. Chen’s Invariants for Real Hypersurfaces in Complex Quadric %D 2018 %J International Electronic Journal of Geometry %P -1307-5624 %V 11 %N 2 %R doi: 10.36890/iejg.545120 %U 10.36890/iejg.545120
ISNAD Bansal, Pooja , Uddin, Siraj , Shahid, Mohammad Hasan . "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
AMA Bansal P. , Uddin S. , Shahid M. H. Extremities Involving B. Y. Chen’s Invariants for Real Hypersurfaces in Complex Quadric. Int. Electron. J. Geom.. 2018; 11(2): 34-46.
Vancouver Bansal P. , Uddin S. , Shahid M. H. Extremities Involving B. Y. Chen’s Invariants for Real Hypersurfaces in Complex Quadric. International Electronic Journal of Geometry. 2018; 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", International Electronic Journal of Geometry, vol. 11, no. 2, pp. 34-46, Nov. 2018, doi:10.36890/iejg.545120