2015/01/01 by Rafik Nasri, Nasri, Rafik
Mathematics · Medicine · Physics and Astronomy · #Advanced Differential Geometry Research #Advanced Neuroimaging Techniques and Applications #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.1501.00308
openalex publication_date 2015/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, We construct the symmetric tensor field Gf1f2 and hf1f2 on a product manifold and we give conditions under which Gf1f2 becomes a metric tensor, theses tensors fields will be called the generalized warped product, and then we develop an expression of curvature for the connection of the generalized warped product in relation to those corresponding analogues of its base and fiber and warping functions. By constructing a frame field in M1×f1f2M2 with respect to the Riemannian metric Gf1f2 and hf1f2, then we calculate the Laplacian-Beltrami operator of a function on a generalized warped product which may be expressed in terms of the local restrictions of the functions to the base and fiber. Finally, we conclude some interesting relationships between the geometry of the couples (M1,g1) and (M2,g2) and that of (M1× M2,hf1f2).