Research and Innovation Articles
Published 2011-01-31
Keywords
- vector bundles,
- frame bundles and connections,
- isometric immersions
How to Cite
Marín Arango, C. A. (2011). Isometric immersions into Riemannian Manifolds. Revista Integración, Temas De matemáticas, 29(1), 31–54. Retrieved from https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/2409
Abstract
This paper summarizes the basic theory of connections in principal bundles and vector bundles in order to apply these theories to the study of isometric immersions in Riemannian manifolds; by an appropriate version ofthe Frobenius theorem we show a result that generalizes the Fundamental Theorem of isometric immersions.
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References
[1] Dajczer M., Submanifolds and isometric immersions, Mathematics Lecture Series, 13, Publish or Perish, Houston, Texas, 1990.
[2] Daniel B., “Isometric immersions into 3-dimensional homogeneous manifolds”, Comment. Math. Helv. 82 (2007), no. 1, 87–131.
[3] Piccione P. and Tausk D., The theory of connections and G–structures. Applications to affine and isometric immersions, XIV Escola de Geometría Diferencial, IMPA, Rio de Janeiro, 2006.
[4] Warner F., Foundations of differentiable manifolds and Lie groups, Graduate Texts in Mathematics, Springer-Verlag, New York, 1983.
[2] Daniel B., “Isometric immersions into 3-dimensional homogeneous manifolds”, Comment. Math. Helv. 82 (2007), no. 1, 87–131.
[3] Piccione P. and Tausk D., The theory of connections and G–structures. Applications to affine and isometric immersions, XIV Escola de Geometría Diferencial, IMPA, Rio de Janeiro, 2006.
[4] Warner F., Foundations of differentiable manifolds and Lie groups, Graduate Texts in Mathematics, Springer-Verlag, New York, 1983.