Role of shape operator in warped product submanifolds of nearly cosymplectic manifolds

Rifaqat Ali; Nadia Alluhaibi; Khaled Mohamed Khedher; Fatemah Mofarreh; Wan Ainun Mior Othman; Rifaqat Ali; Nadia Alluhaibi; Khaled Mohamed Khedher; Fatemah Mofarreh; Wan Ainun Mior Othman

doi:10.3934/math.2020406

AIMS Mathematics

2020, Volume 5, Issue 6: 6313-6324. doi: 10.3934/math.2020406

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Research article

Role of shape operator in warped product submanifolds of nearly cosymplectic manifolds

1.
Department of Mathematics, College of Science and Arts Muhayil, King Khalid University, 9004 Abha, Saudi Arabia
2.
Department of Mathematics, Science and Arts College, Rabigh Campus, King Abdulaziz University, Jeddah, Saudi Arabia
3.
Department of Civil Engineering, College of Engineering, King Khalid University, Abha–61421, KSA, Department of Civil Engineering, ISET, Nabeul, DGET, Tunisia
4.
Mathematical Science Department Faculty of Science Princess Nourah bint Abdulrahman University, Riyadh 11546, Saudi Arabia
5.
Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia

Received: 18 March 2020 Accepted: 15 July 2020 Published: 07 August 2020
MSC : 58C40, 53C42, 35P15

In this paper, first, we find the integrability theorems for the invariant and slant distributions which appeared in the concept of semi-slant submanifolds. Utilizing these theorems, we prove that a semi-slant submanifold reduces to be a warped product semi-slant submanifold, provided some necessary and sufficient conditions concerning the shape operators. Also, it is shown that a few earlier results are exceptional cases of this paper results.
- warped product,
- characterizations,
- integrability conditions,
- shape operators
Citation: Rifaqat Ali, Nadia Alluhaibi, Khaled Mohamed Khedher, Fatemah Mofarreh, Wan Ainun Mior Othman. Role of shape operator in warped product submanifolds of nearly cosymplectic manifolds[J]. AIMS Mathematics, 2020, 5(6): 6313-6324. doi: 10.3934/math.2020406

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Abstract

In this paper, first, we find the integrability theorems for the invariant and slant distributions which appeared in the concept of semi-slant submanifolds. Utilizing these theorems, we prove that a semi-slant submanifold reduces to be a warped product semi-slant submanifold, provided some necessary and sufficient conditions concerning the shape operators. Also, it is shown that a few earlier results are exceptional cases of this paper results.

References

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