Dynamics of principal configurations near umbilics for surfaces in $mathbb(R)^4$

Pages: 664 - 671, Issue Special, July 2003

 Abstract        Full Text (178.1K)              

Matías Navarro - Facultad de Matemáticas, UADY, Calle 8 x 21 S/N, C.P. 97199, Mérida, Yuc., Mexico (email)
Federico Sánchez-Bringas - Departamento de Matemáticas, Facultad de Ciencias, UNAM, Ciudad Universitaria, C.P. 04510, México, D.F., Mexico (email)

Abstract: The $v$-principal configuration of an immersed surface $M$ in $\mathbb(R)^4$ is the set formed by the umbilical points and the lines of principal curvatures with respect to an unitary smooth vector field $v$ normal to $M$. In this article we describe the bifurcation set of $v$-principal configurations of a local surface $M$ depending on two parameters of the surface and depending also on the 1-jet of the vector field $v$ normal to $M$ which defines an isolated simple umbilical point of $M$.

Keywords:  v-principal configuration, umbilics, bifurcation set.
Mathematics Subject Classification:  Primary: 53A05, 34C23; Secondary: 57R25.

Received: September 2002; Published: April 2003.