Year 2020,
, 2028 - 2036, 08.12.2020
Aliya Naaz Sıddıquı
,
Cihan Özgür
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
Aliya Naaz Sıddıquı
,
Cihan Özgür
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.