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

Yıl 2020, Cilt: 49 Sayı: 6, 2028 - 2036, 08.12.2020

Aliya Naaz Sıddıquı , Cihan Özgür

https://doi.org/10.15672/hujms.596699

Cited By: 1

Öz

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.

Anahtar Kelimeler

bi-slant submanifolds, minimal submanifolds, totally geodesic submanifolds, complex space forms

Kaynakça

• [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.