Geometry of Warped Product Semi-Slant Submanifolds of Nearly Kaehler Manifolds

被引：0
作者：
Falleh Rijaullah Al-Solamy
Viqar Azam Khan
Siraj Uddin
机构：
[1] King Abdulaziz University,Department of Mathematics, Faculty of Science
[2] Aligarh Muslim University,Department of Mathematics
来源：
Results in Mathematics | 2017年 / 71卷
关键词：
Warped products; slant submanifold; semi-slant submanifolds; warped product semi-slant submanifolds; nearly Kaehler manifold; 53C40; 53C42; 53C15;
D O I：
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中图分类号：
学科分类号：
摘要：
Non-existence of warped product semi-slant submanifolds of Kaehler manifolds was proved in Sahin (Geom Dedic 117:195–202, 2006), it is interesting to find their existence in a more general setting, e.g., nearly Kaehler manifolds. In this paper, we obtain a necessary and sufficient condition for a semi-slant submanifold of a nearly Kaehler manifold to be a locally warped product. Also, we establish an inequality for the squared norm of the second fundamental form in terms of the warping function and the slant angle. Furthermore, the equality case of the statement is also considered.
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页码：783 / 799
页数：16
相关论文
共 34 条
[1]  
Agricola I.(2006)The Srni lectures on non-integrable geometries with torsion Arch. Math. (Brno) 42 5-84
[2]  
Al-Luhaibi N.S.(2009)CR-warped product submanifolds of nearly Kaehler manifolds J. Korean Math. Soc. 46 979-995
[3]  
Al-Solamy F.R.(2012)Warped product semi-slant submanifolds in Kenmotsu manifolds Turk. J. Math. 36 319-330
[4]  
Khan V.A.(1969)Manifolds of negative curvature Trans. Am. Math. Soc. 145 1-49
[5]  
Atceken M.(2005)Classification des vari’t’s approximativement kähleriennes homog’nes Ann. Glob. Anal. Geom. 27 201-225
[6]  
Bishop R.L.(1990)Slant immersions Bull. Aust. Math. Soc. 41 135-147
[7]  
O’Neill B.(2001)Geometry of warped product CR-submanifolds in Kaehler manifolds Monatsh. Math. 133 177-195
[8]  
Butruille J.B.(2001)Geometry of warped product CR-submanifolds in Kaehler manifolds II Monatsh. Math. 134 103-119
[9]  
Chen B.-Y.(2013)Geometry of warped product submanifolds: a survey J. Adv. Math. Stud. 6 1-43
[10]  
Chen B.-Y.(1985)On the first eigenvalue of the Dirac operator on 6-dimensional manifolds Ann. Glob. Anal. Geom. 3 265-273
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