The Impact of Quasi-Conformal Curvature Tensor on Warped Product Manifolds

被引:0
|
作者
Chen, Bang-Yen [1 ]
Shenawy, Sameh [2 ]
De, Uday Chand [3 ]
Rabie, Alaa [4 ]
Bin Turki, Nasser [5 ]
机构
[1] Michigan State Univ, Dept Math, 619 Red Cedar Rd, E Lansing, MI 48824 USA
[2] Modern Acad Engn & Technol, Basic Sci Dept, Cairo 11571, Egypt
[3] Univ Calcutta, Dept Pure Math, Ballygaunge Circular Rd, Kolkata 700019, W Bengal, India
[4] Fayoum Univ, Fac Sci, Dept Math, Faiyum 63514, Egypt
[5] King Saud Univ, Coll Sci, Dept Math, POB 2455, Riyadh 11451, Saudi Arabia
关键词
warped product; quasi-conformal curvature tensor; Ricci-symmetric manifold; divergence-free; Einstein-like manifold; Cartan-symmetric manifold; SPACETIMES; (K;
D O I
10.3390/axioms13080500
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This work investigates the effects on the factor manifolds of a singly warped product manifold resulting from the presence of a quasi-conformally flat, quasi-conformally symmetric, or divergence-free quasi-conformal curvature tensor. Quasi-conformally flat warped product manifolds exhibit three distinct scenarios: in one scenario, the base manifold has a constant curvature, while in the other two scenarios, it is quasi-Einstein. Alternatively, the fiber manifold has a constant curvature in two scenarios and is Einstein in one scenario. Quasi-conformally symmetric warped product manifolds present three distinct cases: in the first scenario, the base manifold is Ricci-symmetric and the fiber is Einstein; in the second case, the base manifold is Cartan-symmetric and the fiber has constant curvature; and in the last case, the fiber is Cartan-symmetric, and the Ricci tensor of the base manifold is of Codazzi type. Finally, conditions are provided for singly warped product manifolds that admit a divergence-free quasi-conformal curvature tensor to ensure that the Riemann curvature tensors of the factor manifolds are harmonic.
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页数:20
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