Warped Product Pointwise Semi-slant Submanifolds of Sasakian Manifol Retracted
Download PDF
Authors: A. BOUTIARA
DOI: 10.46793/KgJMat2105.721M
Abstract:
Recently, B.-Y. Chen and O. J. Garay studied pointwise slant submanifolds of almost Hermitian manifolds. By using the notion of pointwise slant submanifolds, we investigate the geometry of pointwise semi-slant submanifolds and their warped products in Sasakian manifolds. We give non-trivial examples of such submanifolds and obtain several fundamental results, including a characterization for warped product pointwise semi-slant submanifolds of Sasakian manifolds.
Keywords:
Warped products, pointwise slant submanifolds, pointwise semi-slant submanifolds, Sasakian manifolds.
References:
[1] F. R. Al-Solamy and V. A. Khan, Warped product semi-slant submanifolds of a Sasakian manifold, Serdica Math. J. 34 (2008), 597–606.
[2] F. R. Al-Solamy, V. A. Khan and S. Uddin, Geometry of warped product semi-slant submanifolds of nearly Kaehler manifolds, Results Math. 71 (2017), 783–799.
[3] R. L. Bishop and B. O’Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969), 1–49.
[4] D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Mathematics 509, Springer-Verlag, New York, 1976.
[5] J. L. Cabrerizo, A. Carriazo, L. M. Fernandez and M. Fernandez, Semi-slant submanifolds of a Sasakian manifold, Geom. Dedicata 78 (1999), 183–199.
[6] J. L. Cabrerizo, A. Carriazo, L. M. Fernandez and M. Fernandez, Slant submanifolds in Sasakian manifolds, Glasg. Math. J. 42 (2000), 125–138.
[7] B.-Y. Chen, Slant immersions, Bull. Aust. Math. Soc. 41 (1990), 135–147.
[8] B.-Y. Chen, Geometry of Slant Submanifolds, Katholieke Universiteit, Leuven, 1990.
[9] B.-Y. Chen, Geometry of warped product CR-submanifolds in Kaehler manifolds, Monatsh. Math. 133 (2001), 177–195.
[10] B.-Y. Chen, Geometry of warped product CR-submanifolds in Kaehler manifolds II, Monatsh. Math. 134 (2001), 103–119.
[11] B.-Y. Chen, Pseudo-Riemannian Geometry, δ-Invariants and Applications, World Scientific, Hackensack, New Jersey, 2011.
[12] B.-Y. Chen, Geometry of warped product submanifolds: a survey, J. Adv. Math. Stud. 6(2) (2013), 1–43.
[13] B.-Y. Chen, Differential Geometry of Warped Product Manifolds and Submanifolds, World Scientific, Hackensack, New Jersey, 2017.
[14] B.-Y. Chen and O. Garay, Pointwise slant submanifolds in almost Hermitian manifolds, Turkish J. Math. 36 (2012), 630–640.
[15] B.-Y. Chen and S. Uddin, Warped product pointwise bi-slant submanifolds of Kaehler manifolds, Publ. Math. Debrecen 92(1) (2018), 1–16.
[16] F. Etayo, On quasi-slant submanifolds of an almost Hermitian manifold, Publ. Math. Debrecen 53 (1998), 217–223.
[17] I. Hasegawa and I. Mihai, Contact CR-warped product submanifolds in Sasakian manifolds, Geom. Dedicata 102 (2003), 143–150.
[18] S. Hiepko, Eine inner kennzeichungder verzerrten produkte, Math. Ann. 241 (1979), 209–215.
[19] K. A. Khan, V. A. Khan and S. Uddin, Warped product submanifolds of cosymplectic manifolds, Balkan J. Geom. Appl. 13 (2008), 55–65.
[20] A. Lotta, Slant submanifolds in contact geometry, Bull. Math. Soc. Roumanie 39 (1996), 183–198.
[21] M. I. Munteanu, Warped product contact CR-submanifolds of Sasakian space forms, Publ. Math. Debrecen 66 (2005), 75–120.
[22] N. Papaghiuc, Semi-slant submanifolds of Kaehlerian manifold, Ann. Şt. Univ. Iaşi 9 (1994), 55–61.
[23] K. S. Park, Pointwise almost h-semi-slant submanifolds, Int. J. Math. 26 (2015), Article ID 1550099.
[24] B. Sahin, Non existence of warped product semi-slant submanifolds of Kaehler manifolds, Geom. Dedicata 117 (2006), 195–202.
[25] B. Sahin, Warped product submanifolds of Kaehler manifolds with a slant factor, Ann. Pol. Math. 95 (2009), 207–226.
[26] B. Sahin, Warped product pointwise semi-slant submanifolds of Kaehler manifolds, Port. Math. 70 (2013), 252–268.
[27] S. Uddin, V. A. Khan and H. H. Khan, Some results on warped product submanifolds of a Sasakian manifold, Int. J. Math. Math. Sci. (2010), Article ID 743074 DOI 10.1155/2010/743074.
[28] S. Uddin and F. R. Al-Solamy, Warped product pseudo-slant submanifolds of cosymplectic manifolds, An. Ştiinţ. Univ. Al. I. Cuza Iaşi Mat (N.S.) Tome LXIII, 3 (2016), 901–913.
[29] S. Uddin and F. R. Al-Solamy, Warped product pseudo-slant immersions in Sasakian manifolds, Publ. Math. Debrecen 91(3-4) (2017), 331–348.
[30] S. Uddin, B.-Y. Chen and F. R. Al-Solamy, Warped product bi-slant immersions in Kaehler manifolds, Mediterr. J. Math. 14(95) (2017), DOI 10.1007/s00009-017-0896-8.
[31] S. Uddin and A. H. Alkhaldi, Pointwise slant submanifolds and their warped products in Sasakian manifolds, Filomat 32(12) (2018), 1–12.
[32] K. Yano and M. Kon, Structures on Manifolds, Series in Pure Mathematics, World Scientific Publishing Co., Singapore, 1984.