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

#### Ali H. ALKHALDİ [1] , Akram ALİ [2] , Mehmet Akif AKYOL [3]

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.
CR-warped product, warped product, pointwise semi-slant submanifold, modified inequality, Kaehler manifold
• [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.
Primary Language en Mathematics Mathematics Orcid: 0000-0002-6053-3032Author: Ali H. ALKHALDİInstitution: King Khalid UniversityCountry: Saudi Arabia Orcid: 0000-0002-6053-3031Author: Akram ALİ (Primary Author)Institution: King Khalid UniversityCountry: Saudi Arabia Orcid: 0000-0003-2334-6955Author: Mehmet Akif AKYOLInstitution: BINGOL UNIVERSITYCountry: Turkey King Khalid University R.G.P.2/57/40 The authors extend their appreciation to the deanship of scientific research at King Khalid University for funding this work through research groups program. Publication Date : June 7, 2021
 Bibtex @research article { hujms585465, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2021}, volume = {50}, pages = {634 - 646}, doi = {10.15672/hujms.585465}, title = {Some remarks on a family of warped product pointwise semi-slant submanifolds of Kaehler manifold}, key = {cite}, author = {Alkhaldi, Ali H. and Ali, Akram and Akyol, Mehmet Akif} } APA Alkhaldi, A , Ali, A , Akyol, M . (2021). Some remarks on a family of warped product pointwise semi-slant submanifolds of Kaehler manifold . Hacettepe Journal of Mathematics and Statistics , 50 (3) , 634-646 . DOI: 10.15672/hujms.585465 MLA Alkhaldi, A , Ali, A , Akyol, M . "Some remarks on a family of warped product pointwise semi-slant submanifolds of Kaehler manifold" . Hacettepe Journal of Mathematics and Statistics 50 (2021 ): 634-646 Chicago Alkhaldi, A , Ali, A , Akyol, M . "Some remarks on a family of warped product pointwise semi-slant submanifolds of Kaehler manifold". Hacettepe Journal of Mathematics and Statistics 50 (2021 ): 634-646 RIS TY - JOUR T1 - Some remarks on a family of warped product pointwise semi-slant submanifolds of Kaehler manifold AU - Ali H. Alkhaldi , Akram Ali , Mehmet Akif Akyol Y1 - 2021 PY - 2021 N1 - doi: 10.15672/hujms.585465 DO - 10.15672/hujms.585465 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 634 EP - 646 VL - 50 IS - 3 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.585465 UR - https://doi.org/10.15672/hujms.585465 Y2 - 2020 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Some remarks on a family of warped product pointwise semi-slant submanifolds of Kaehler manifold %A Ali H. Alkhaldi , Akram Ali , Mehmet Akif Akyol %T Some remarks on a family of warped product pointwise semi-slant submanifolds of Kaehler manifold %D 2021 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 50 %N 3 %R doi: 10.15672/hujms.585465 %U 10.15672/hujms.585465 ISNAD Alkhaldi, Ali H. , Ali, Akram , Akyol, Mehmet Akif . "Some remarks on a family of warped product pointwise semi-slant submanifolds of Kaehler manifold". Hacettepe Journal of Mathematics and Statistics 50 / 3 (June 2021): 634-646 . https://doi.org/10.15672/hujms.585465 AMA Alkhaldi A , Ali A , Akyol M . Some remarks on a family of warped product pointwise semi-slant submanifolds of Kaehler manifold. Hacettepe Journal of Mathematics and Statistics. 2021; 50(3): 634-646. Vancouver Alkhaldi A , Ali A , Akyol M . Some remarks on a family of warped product pointwise semi-slant submanifolds of Kaehler manifold. Hacettepe Journal of Mathematics and Statistics. 2021; 50(3): 634-646. IEEE A. Alkhaldi , A. Ali and M. Akyol , "Some remarks on a family of warped product pointwise semi-slant submanifolds of Kaehler manifold", Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 3, pp. 634-646, Jun. 2021, doi:10.15672/hujms.585465

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