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Year 2020, , 2028 - 2036, 08.12.2020
https://doi.org/10.15672/hujms.596699

Abstract

References

  • [1] K. Abe, Applications of Riccati type differential equation to Riemannian manifolds with totally geodesic distributions, Tohoku Math. J. 25 (2), 425–444, 1973.
  • [2] A. Bejancu, Geometry of CR-submanifolds, Mathematics and its Applications, (East European Series), 23. D. Reidel Publishing Co., Dordrecht, 1986.
  • [3] A. Bejancu, M. Kon and K. Yano, CR-submanifolds of a complex space form, J. Differential Geom. 16 (1) 137–145, 1981.
  • [4] J.L. Cabrerizo, A. Carriazo, L.M. Fernández and M. Fernández, Semi-slant submanifolds of a Sasakian manifold, Geom. Dedicata 78 (2), 183–199, 1999.
  • [5] J.L. Cabrerizo, A. Carriazo, L.M. Fernández and M. Fernández, Slant submanifolds in Sasakian manifolds, Glasg. Math. J. 42 (1), 125–138, 2000.
  • [6] J.L. Cabrerizo, A. Carriazo, L.M. Fernández and M. Fernández, Structure on slant submanifold of a contact manifold, Indian J. Pure Appl. Math. 31 (7), 857–864, 2000.
  • [7] A. Carriazo, Bi-slant immersions, in: Proc. ICRAMS, 88–97, Kharagpur, India, 2000.
  • [8] B.-Y. Chen, Geometry of Submanifolds, Pure and Applied Mathematics, No. 22. Marcel Dekker, Inc., New York, 1973.
  • [9] B.-Y. Chen, Geometry of slant submanifolds, Katholieke Universiteit Leuven, Louvain, 1990.
  • [10] B.-Y. Chen, Slant immersions, Bull. Aust. Math. Soc. 41 (1), 135–147, 1990.
  • [11] B.-Y. Chen and D.E. Blair, On CR submanifolds of Hermitian manifolds, Israel J. Math. 34 (4), 353–363, 1979.
  • [12] B.-Y. Chen and S. Uddin, Warped product pointwise bi-slant submanifolds of Kaehler manifolds, Publ. Math. Debrecen 92, (1-2), 183–199, 2018.
  • [13] M. Gülbahar, E. Kılıç, and S. Keleş, A useful orthonormal basis on bi-slant submanifolds of almost Hermitian manifolds, Tamkang J. Math. 47 (2), 143–161, 2016.
  • [14] T. Ikawa, On submanifolds in a space with Sasakian 3-structure, Colloq. Math. 47 (1), 47–57, 1982.
  • [15] T. Ikawa, On some C-totally real submanifolds in a space with Sasakian 3-structure, Colloq. Math. 49 (1), 27–32, 1984.
  • [16] A. Mihai and I. Mihai, CR-submanifolds in complex and Sasakian space forms, in: Geometry of Cauchy-Riemann Submanifolds, 217–266, Springer, Singapore, 2016.
  • [17] N. Papaghiuc, Semi-slant submanifolds of a Kaehlerian manifold, An. Ştiinţ Al. I. Cuza Iaşi. Mat. 40 (1), 55–61, 1994.
  • [18] A.N. Siddiqui, M.H. Shahid and M. Jamali, Simons’ type formula for Kaehlerian slant submanifolds in complex space forms, Kyungpook Math. J. 58 (1), 149–165, 2018.
  • [19] J. Simons, Minimal varieties in Riemannian manifolds, Ann. Math. 88 (2), 62–105, 1968.
  • [20] B. Şahin, Warped product submanifolds of Kaehler manifolds with a slant factor, Ann. Polon. Math. 95 (3), 207–226, 2009.
  • [21] S. Yamaguchi, M. Kon and T. Ikawa, C-totally real submanifolds, J. Differential Geometry, 11 (1), 59–64, 1976.
  • [22] K. Yano and M. Kon, CR submanifolds of Kaehlerian and Sasakian manifolds, Progress in Mathematics, 30. Birkhäuser, Boston, Mass., 1983.
  • [23] K. Yano and M. Kon, Structures on manifolds, Series in Pure Mathematics, 3. World Scientific Publishing Co., Singapore, 1984.

An integral formula for bi-slant submanifolds in complex space forms

Year 2020, , 2028 - 2036, 08.12.2020
https://doi.org/10.15672/hujms.596699

Abstract

The present paper deals with bi-slant submanifolds in complex space forms. We obtain an integral formula of Simons' type for bi-slant submanifolds of a complex space form with positive constant holomorphic sectional curvature. Then, we apply it to prove our main result. We also discuss the same result in different submanifolds such as hemi-slant and semi-slant submanifolds.

References

  • [1] K. Abe, Applications of Riccati type differential equation to Riemannian manifolds with totally geodesic distributions, Tohoku Math. J. 25 (2), 425–444, 1973.
  • [2] A. Bejancu, Geometry of CR-submanifolds, Mathematics and its Applications, (East European Series), 23. D. Reidel Publishing Co., Dordrecht, 1986.
  • [3] A. Bejancu, M. Kon and K. Yano, CR-submanifolds of a complex space form, J. Differential Geom. 16 (1) 137–145, 1981.
  • [4] J.L. Cabrerizo, A. Carriazo, L.M. Fernández and M. Fernández, Semi-slant submanifolds of a Sasakian manifold, Geom. Dedicata 78 (2), 183–199, 1999.
  • [5] J.L. Cabrerizo, A. Carriazo, L.M. Fernández and M. Fernández, Slant submanifolds in Sasakian manifolds, Glasg. Math. J. 42 (1), 125–138, 2000.
  • [6] J.L. Cabrerizo, A. Carriazo, L.M. Fernández and M. Fernández, Structure on slant submanifold of a contact manifold, Indian J. Pure Appl. Math. 31 (7), 857–864, 2000.
  • [7] A. Carriazo, Bi-slant immersions, in: Proc. ICRAMS, 88–97, Kharagpur, India, 2000.
  • [8] B.-Y. Chen, Geometry of Submanifolds, Pure and Applied Mathematics, No. 22. Marcel Dekker, Inc., New York, 1973.
  • [9] B.-Y. Chen, Geometry of slant submanifolds, Katholieke Universiteit Leuven, Louvain, 1990.
  • [10] B.-Y. Chen, Slant immersions, Bull. Aust. Math. Soc. 41 (1), 135–147, 1990.
  • [11] B.-Y. Chen and D.E. Blair, On CR submanifolds of Hermitian manifolds, Israel J. Math. 34 (4), 353–363, 1979.
  • [12] B.-Y. Chen and S. Uddin, Warped product pointwise bi-slant submanifolds of Kaehler manifolds, Publ. Math. Debrecen 92, (1-2), 183–199, 2018.
  • [13] M. Gülbahar, E. Kılıç, and S. Keleş, A useful orthonormal basis on bi-slant submanifolds of almost Hermitian manifolds, Tamkang J. Math. 47 (2), 143–161, 2016.
  • [14] T. Ikawa, On submanifolds in a space with Sasakian 3-structure, Colloq. Math. 47 (1), 47–57, 1982.
  • [15] T. Ikawa, On some C-totally real submanifolds in a space with Sasakian 3-structure, Colloq. Math. 49 (1), 27–32, 1984.
  • [16] A. Mihai and I. Mihai, CR-submanifolds in complex and Sasakian space forms, in: Geometry of Cauchy-Riemann Submanifolds, 217–266, Springer, Singapore, 2016.
  • [17] N. Papaghiuc, Semi-slant submanifolds of a Kaehlerian manifold, An. Ştiinţ Al. I. Cuza Iaşi. Mat. 40 (1), 55–61, 1994.
  • [18] A.N. Siddiqui, M.H. Shahid and M. Jamali, Simons’ type formula for Kaehlerian slant submanifolds in complex space forms, Kyungpook Math. J. 58 (1), 149–165, 2018.
  • [19] J. Simons, Minimal varieties in Riemannian manifolds, Ann. Math. 88 (2), 62–105, 1968.
  • [20] B. Şahin, Warped product submanifolds of Kaehler manifolds with a slant factor, Ann. Polon. Math. 95 (3), 207–226, 2009.
  • [21] S. Yamaguchi, M. Kon and T. Ikawa, C-totally real submanifolds, J. Differential Geometry, 11 (1), 59–64, 1976.
  • [22] K. Yano and M. Kon, CR submanifolds of Kaehlerian and Sasakian manifolds, Progress in Mathematics, 30. Birkhäuser, Boston, Mass., 1983.
  • [23] K. Yano and M. Kon, Structures on manifolds, Series in Pure Mathematics, 3. World Scientific Publishing Co., Singapore, 1984.
There are 23 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Aliya Naaz Sıddıquı 0000-0003-3895-7548

Cihan Özgür 0000-0002-4579-7151

Publication Date December 8, 2020
Published in Issue Year 2020

Cite

APA Sıddıquı, A. N., & Özgür, C. (2020). An integral formula for bi-slant submanifolds in complex space forms. Hacettepe Journal of Mathematics and Statistics, 49(6), 2028-2036. https://doi.org/10.15672/hujms.596699
AMA Sıddıquı AN, Özgür C. An integral formula for bi-slant submanifolds in complex space forms. Hacettepe Journal of Mathematics and Statistics. December 2020;49(6):2028-2036. doi:10.15672/hujms.596699
Chicago Sıddıquı, Aliya Naaz, and Cihan Özgür. “An Integral Formula for Bi-Slant Submanifolds in Complex Space Forms”. Hacettepe Journal of Mathematics and Statistics 49, no. 6 (December 2020): 2028-36. https://doi.org/10.15672/hujms.596699.
EndNote Sıddıquı AN, Özgür C (December 1, 2020) An integral formula for bi-slant submanifolds in complex space forms. Hacettepe Journal of Mathematics and Statistics 49 6 2028–2036.
IEEE A. N. Sıddıquı and C. Özgür, “An integral formula for bi-slant submanifolds in complex space forms”, Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 6, pp. 2028–2036, 2020, doi: 10.15672/hujms.596699.
ISNAD Sıddıquı, Aliya Naaz - Özgür, Cihan. “An Integral Formula for Bi-Slant Submanifolds in Complex Space Forms”. Hacettepe Journal of Mathematics and Statistics 49/6 (December 2020), 2028-2036. https://doi.org/10.15672/hujms.596699.
JAMA Sıddıquı AN, Özgür C. An integral formula for bi-slant submanifolds in complex space forms. Hacettepe Journal of Mathematics and Statistics. 2020;49:2028–2036.
MLA Sıddıquı, Aliya Naaz and Cihan Özgür. “An Integral Formula for Bi-Slant Submanifolds in Complex Space Forms”. Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 6, 2020, pp. 2028-36, doi:10.15672/hujms.596699.
Vancouver Sıddıquı AN, Özgür C. An integral formula for bi-slant submanifolds in complex space forms. Hacettepe Journal of Mathematics and Statistics. 2020;49(6):2028-36.