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Infinitesimal Variations of Submanifolds.
- Source :
- Bulletin of the Brazilian Mathematical Society; Sep2021, Vol. 52 Issue 3, p573-589, 17p
- Publication Year :
- 2021
-
Abstract
- This paper deals with the subject of infinitesimal variations of Euclidean submanifolds with arbitrary dimension and codimension. The main goal is to establish a Fundamental theorem for these geometric objects. Similar to the theory of isometric immersions in Euclidean space, we prove that a system of three equations for a certain pair of tensors are the integrability conditions for the differential equation that determines the infinitesimal variations. In addition, we give some rigidity results when the submanifold is intrinsically a Riemannian product of manifolds. [ABSTRACT FROM AUTHOR]
- Subjects :
- RIEMANNIAN manifolds
DIFFERENTIAL equations
SUBMANIFOLDS
GOAL (Psychology)
EQUATIONS
Subjects
Details
- Language :
- English
- ISSN :
- 16787544
- Volume :
- 52
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Bulletin of the Brazilian Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 151566676
- Full Text :
- https://doi.org/10.1007/s00574-020-00220-x