Back to Search
Start Over
Geometric properties of normal submanifolds
- Source :
- Boletín de la Sociedad Matemática Mexicana. 26:1273-1288
- Publication Year :
- 2020
- Publisher :
- Springer Science and Business Media LLC, 2020.
-
Abstract
- This paper deals with normal submanifolds immersed in a Riemannian manifold $${\overline{M}}$$ . We generalized some recent results of surfaces in space forms obtained by Hernandez-Lamoneda and Ruiz-Hernandez (Bull Braz Marh Soc (NS) 49:447–462, 2018) to arbitrary submanifolds. More precisely, given a submanifold M in $${\overline{M}}$$ , we study the submanifolds formed by orthogonal geodesics to M, and call it a ruled normal submanifold to M. In the first part of this paper, we analyze these submanifolds and establish some geometric properties of them. Furthermore, we extend some properties about the lines of curvature and using the ideas of [3] also give an extension of the classical Theorem of Bonnet to hypersurfaces of $${\overline{M}}$$ .
- Subjects :
- Pure mathematics
Overline
Geodesic
Mathematics::Complex Variables
General Mathematics
010102 general mathematics
Extension (predicate logic)
Riemannian manifold
Space (mathematics)
Curvature
Submanifold
01 natural sciences
010101 applied mathematics
Mathematics::Differential Geometry
0101 mathematics
Classical theorem
Mathematics::Symplectic Geometry
Mathematics
Subjects
Details
- ISSN :
- 22964495 and 1405213X
- Volume :
- 26
- Database :
- OpenAIRE
- Journal :
- Boletín de la Sociedad Matemática Mexicana
- Accession number :
- edsair.doi...........7d8caf3aded9226e9009f92da09cafb2