Geodesic
Sequential warped product submanifolds in locally product Riemannian manifolds
Filomat, Tome 37 (2023) no. 27, p. 9259

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DOI

In this paper, we present sequential warped product submanifolds of locally product Riemannian manifolds and show that there exists a class of non-trivial sequential warped product submanifolds of a locally product Riemannian manifold of the form (M θ × σ 1 M ⊥) × σ 2 M T by giving non-trivial examples. Also, we prove some useful results for such warped products and establish Chen's inequality which represents a relationship between the squared norm of the second fundamental form for the warping functions σ 1 and σ 2. Further, some applications of our main result are given.
DOI : 10.2298/FIL2327259A
Classification : 53C15, 53C40, 53C42, 53B25, 53C21 53C25, 53C50
Keywords: Slant submanifolds, mixed geodesic, skew semi-invariant submanifolds, bi-warped products, sequential warped products, locally product Riemannian manifolds 
Najwa Mohammed Al-Asmari; Siraj Uddin; Monia Fouad Naghi. Sequential warped product submanifolds in locally product Riemannian manifolds. Filomat, Tome 37 (2023) no. 27, p. 9259 . doi: 10.2298/FIL2327259A
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     author = {Najwa Mohammed Al-Asmari and Siraj Uddin and Monia Fouad Naghi},
     title = {Sequential warped product submanifolds in locally product {Riemannian} manifolds},
     journal = {Filomat},
     pages = {9259 },
     year = {2023},
     volume = {37},
     number = {27},
     doi = {10.2298/FIL2327259A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2327259A/}
}
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