Isometric immersions in codimension two of warped products into space forms

2004/07/22 by Marcos Dajczer, M. Dajczer, Ruy Tojeiro +3
Engineering · Mathematics · #3D Shape Modeling and Analysis #53B25 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematics and Applications #math.DG #msc:53B25

paper · pdf · doi:10.48550/arxiv.math/0407389

35 pages

arxiv created 2004/07/22 · openalex publication_date 2004/07/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a local classification of isometric immersions f\colon L^p×_ρMⁿ→\Q_c^p+n+k in codimensions k=1, 2 of warped products of Riemannian manifolds into space forms, under the assumptions that n≥ k+1 and that N^p+n=L^p×_ρMⁿ has no points with the same constant sectional curvature c as the ambient space form.

Related

• Isometric immersions of warped products
• On the estimates of warping functions on isometric immersions
• Geometry of submanifolds with respect to ambient vector fields
• A fundamental theorem for submanifolds in semi-Riemannian warped products
• A decomposition theorem for immersions of product manifolds