Isometric immersions into manifolds with metallic structures

2017/06/29 by Julien Roth, Abhitosh Upadhyay, Roth, Julien +1
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1706.09596

openalex publication_date 2017/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider submanifolds into Riemannian manifold with metallic structures. We obtain some new results for hypersurfaces in these spaces and we express the fundamental theorem of submanifolds into products spaces in terms of metallic structures. Moreover, we define new structures called complex metallic structures. We show that these structures are linked with complex structures. Then, we consider submanifolds into Riemannian manifold with such structures with a focus on invariant submanifolds and hypersurfaces. We also express in particular the fundamental theorem of submanifolds of complex space form in terms of complex metallic structures.

Citations

• A Bonnet theorem for isometric immersions into products of space forms

Related

• Submanifolds in metallic Riemannian manifolds
• Invariant, anti-invariant and slant submanifolds of a metallic Riemannian manifold
• Induced structures on submanifolds in almost product Riemannian manifolds
• Slant and semi-slant submanifolds in metallic Riemannian manifolds
• Remarks on metallic warped product manifolds