Some remarks on a family of warped product pointwise semi-slant submanifolds of Kaehler manifold

Yıl 2021, Cilt: 50 Sayı: 3, 634 - 646, 07.06.2021

Ali H. Alkhaldi Akram Ali Mehmet Akif Akyol

https://doi.org/10.15672/hujms.585465

Cited By: 1

Öz

The purpose of this paper is to provide the complete classifications of the second fundamental form inequality for a warped product pointwise semi-slant submanifold in a Kaehler manifold which was obtained by Şahin [Th. 5.2, Warped product pointwise semi-slant submanifold of Kaehler manifold, Port. Math. 2013] in terms of intrinsic and extrinsic invariants. In this paper, we give some conditions that are not addressed or considered in the cited paper mentioned above. Finally, we provide necessary and sufficient conditions that satisfy inequalities' equalities.

Anahtar Kelimeler

CR-warped product, warped product, pointwise semi-slant submanifold, modified inequality, Kaehler manifold

Destekleyen Kurum

King Khalid University

Proje Numarası

R.G.P.2/57/40

Teşekkür

The authors extend their appreciation to the deanship of scientific research at King Khalid University for funding this work through research groups program.

Kaynakça

• [1] A. Ali, and P. Laurian-Ioan, Geometry of warped product immersion of Kenmotsu space forms and its application to slant immersions, J. Geom. Phy. 114, 276-290, 2017.
• [2] A. Ali and P. Laurian-Ioan, Geometric classification of warped products isometrically immersed into Sasakian space forms, Math. Nachr. 292, 234–251, 2019.
• [3] A. Ali, and C. Özel, Geometry of warped product pointwise semi-slant submanifolds of cosymplectic manifolds and its applications, Int. J. Geom. Methods Mod. Phys. 14, 1750042, 2017.
• [4] A. Ali, S. Uddin, and W.A.M. Othman, Geometry of warped product pointwise semislant submanifolds of Kaehler manifolds, Filomat 32 (12), 3771-3788, 2017.
• [5] R.L. Bishop, and B. O’Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145, 1-9, 1969.
• [6] O. Calin and D.C. Chang, Geometric mechanics on Riemannian manifolds: applications to partial differential equations, Springer Science & Business Media, 2006.
• [7] B.-Y. Chen, Geometry of warped product CR-submanifold in Kaehler manifolds I, Monatsh. Math. 133, 177-195, 2001.
• [8] B.-Y. Chen, Another general inequality for warped product CR-warped product submanifold in complex space forms, Hokkaido Math. J. 32, 415-444, 2003.
• [9] B.-Y. Chen, and O. Garay, Pointwise slant submanifolds in almost Hermitian manifolds, Turkish J. Math. 36, 630-640, 2012.
• [10] F. Etayo, On quasi-slant submanifolds of an almost Hermitian manifold, Publ. Math. Debrecen 53, 217-223, 1998.
• [11] A. Mustafa, Geometry of warped product submanifolds of Riemannian manifolds, PhD thesis, University of Malaya, 2016.
• [12] J. Nash, The imbedding problem for Riemannian manifolds, Ann. of Math. 63, 2063, 1956.
• [13] N. Papaghiuc, Semi-slant submanifold of Kaehler manifold, An. St. Univ. Al. I. Cuza. Iasi. 40, 55-61, 1994.
• [14] B. Şahin, Non-existence of warped product semi-slant submanifolds of Kaehler manifolds, Geom. Dedicata 117, 95202, 2006.
• [15] B. Şahin, Warped product pointwise semi-slant submanifold of Kaehler manifold, Port. Math. 70, 251-268, 2013.
• [16] M.M. Tripathi, Improved Chen-Ricci inequality for curvature-like tensors and its applications, Diff. Geom. Appl. 29, 685-698, 2011.
• [17] M. M. Tripathi, C-totally real warped product submanifolds, An. St. Univ. Al. I. Cuza. Iasi 58 (2), 417-436, 2012.
• [18] B. Ünal, Multiply Warped Products, J. Geom. Phy. 34 (3-4), 287-301, 2000.
• [19] K. Yano and M. Kon, Structures on manifolds, World Scientific, 1984.