First chen inequality for biwarped product submanifold of a Riemannian space forms

Biswabismita Bag; Meraj Ali Khan; Tanumoy Pal; Shyamal Kumar Hui; Biswabismita Bag; Meraj Ali Khan; Tanumoy Pal; Shyamal Kumar Hui

doi:10.3934/math.2025454

AIMS Mathematics

2025, Volume 10, Issue 4: 9917-9932. doi: 10.3934/math.2025454

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First chen inequality for biwarped product submanifold of a Riemannian space forms

1.
Department of Mathematics, The University of Burdwan, Golapbag, Burdwan 713104, West Bengal, India; your.bidisa123@gmail.com, skhui@math.buruniv.ac.in
2.
Department of Mathematics and statistics, Imam Mohammad Ibn Saud Islamic University, Riyadh 11566, Saudi Arabia
3.
High School, Mankhamar, Bankura 722144, West Bengal, India; tanumoypalmath@gmail.com

Received: 22 January 2025 Revised: 12 April 2025 Accepted: 23 April 2025 Published: 27 April 2025
MSC : 53B25, 53C40, 53C42, 53Z05

Within this paper, we have formulated the first Chen inequality for bi-warped product sub-manifolds within Riemannian space forms. This inequality intricately involved extrinsic invariants such as mean curvature and the lengths of the warping functions, while also incorporating intrinsic invariants like sectional curvature and $ \delta $-invariants. Furthermore, we extensively explored and analyzed the scenarios where equality conditions were met within the context of this inequality.
- bi-warped product,
- mean curvature,
- $ \delta $-invariant,
- scalar curvature,
- minimal sub-manifolds,
- Riemannian space forms,
- submanifolds
Citation: Biswabismita Bag, Meraj Ali Khan, Tanumoy Pal, Shyamal Kumar Hui. First chen inequality for biwarped product submanifold of a Riemannian space forms[J]. AIMS Mathematics, 2025, 10(4): 9917-9932. doi: 10.3934/math.2025454

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Abstract

Within this paper, we have formulated the first Chen inequality for bi-warped product sub-manifolds within Riemannian space forms. This inequality intricately involved extrinsic invariants such as mean curvature and the lengths of the warping functions, while also incorporating intrinsic invariants like sectional curvature and $ \delta $-invariants. Furthermore, we extensively explored and analyzed the scenarios where equality conditions were met within the context of this inequality.

References

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