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July  2003, 9(4): 877-900. doi: 10.3934/dcds.2003.9.877

Simple umbilic points on surfaces immersed in $\R^4$

Carlos Gutierrez 1, and  Víctor Guíñez 2,

1. 

ICMC-USP, São Carlos, Caixa Postal 668, CEP 13560-970, São Carlos, SP, Brazil
2. 

Universidad de Santiago de Chile, Departamento de Matemática y C.C., Casilla 307, Correo 2, Santiago, Chile

Received  November 2001 Revised  December 2002 Published  April 2003

We study local problems around simple umbilic points of surfaces immersed in $\mathbb R^4$ such as finite determinacy and versal unfoldings.
Keywords: quartic differential forms., umbilic points, Lines of curvature, smooth immersions.
Mathematics Subject Classification: 53A07, 58D10, 37G1.
Citation: Carlos Gutierrez, Víctor Guíñez. Simple umbilic points on surfaces immersed in $\R^4$. Discrete and Continuous Dynamical Systems, 2003, 9 (4) : 877-900. doi: 10.3934/dcds.2003.9.877
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