A fundamental theorem for submanifolds of multiproducts of real space forms
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Marie-Amélie Lawn
Abstract
We prove a Bonnet theorem for isometric immersions of submanifolds into the products of an arbitrary number of simply connected real space forms. Then we prove the existence of associate families of minimal surfaces in such products. Finally, in the case of đť•Š2 Ă— đť•Š2, we give a complex version of the main theorem in terms of the two canonical complex structures of đť•Š2 Ă— đť•Š2.
Acknowledgements
The authors want to thank F. Torralbo for helpful discussions and the referee for many valuable comments which make this paper more readable.
References
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Articles in the same Issue
- Frontmatter
- Classification of 3-dimensional left-invariant almost paracontact metric structures
- On the topology of the spaces of curvature constrained plane curves
- On deformations of parallel G2 structures and almost contact metric structures
- A flag representation of projection functions
- A fundamental theorem for submanifolds of multiproducts of real space forms
- Intriguing sets of quadrics in PG(5, q)
- Successive radii and ball operators in generalized Minkowski spaces
- Optimal inequalities for the normalized δ-Casorati curvatures of submanifolds in Kenmotsu space forms
- The Archimedean projection property
- Kernels of numerical pushforwards
- Modified classical flat Minkowski planes
Articles in the same Issue
- Frontmatter
- Classification of 3-dimensional left-invariant almost paracontact metric structures
- On the topology of the spaces of curvature constrained plane curves
- On deformations of parallel G2 structures and almost contact metric structures
- A flag representation of projection functions
- A fundamental theorem for submanifolds of multiproducts of real space forms
- Intriguing sets of quadrics in PG(5, q)
- Successive radii and ball operators in generalized Minkowski spaces
- Optimal inequalities for the normalized δ-Casorati curvatures of submanifolds in Kenmotsu space forms
- The Archimedean projection property
- Kernels of numerical pushforwards
- Modified classical flat Minkowski planes
