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Inflection points and topology of surfaces in 4-space
Author(s):
Ronaldo
Alves
Garcia;
Dirce
Kiyomi Hayashida
Mochida;
Maria
del Carmen
Romero Fuster;
Maria
Aparecida
Soares Ruas
Journal:
Trans. Amer. Math. Soc.
352
(2000),
3029-3043.
MSC (1991):
Primary 58C27;
Secondary 53A05
Posted:
March 15, 2000
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Abstract:
We consider asymptotic line fields on generic surfaces in 4-space and show that they are globally defined on locally convex surfaces, and their singularities are the inflection points of the surface. As a consequence of the generalized Poincaré-Hopf formula, we obtain some relations between the number of inflection points in a generic surface and its Euler number. In particular, it follows that any 2-sphere, generically embedded as a locally convex surface in 4-space, has at least 4 inflection points.
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Additional Information:
Ronaldo
Alves
Garcia
Affiliation:
Instituto de Matemática e Estatistica, Universidade Federal de Goiás, 74001-970, Goiânia, GO, Brazil
Email:
ragarcia@mat.ufg.br
Dirce
Kiyomi Hayashida
Mochida
Affiliation:
Departamento de Matemática, Universidade Federal de São Carlos, 13560-905, São Carlos, SP, Brazil
Email:
dirce@dm.ufscar.br
Maria
del Carmen
Romero Fuster
Affiliation:
Departamento de Geometria e Topologia, Universidad de Valencia, 46000, Valencia, Spain
Email:
romero@uv.es
Maria
Aparecida
Soares Ruas
Affiliation:
Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Departamento de Matemática, Caixa Postal 668, 13560-970, São Carlos, SP, Brazil
Email:
maasruas@icmsc.sc.usp.br
DOI:
10.1090/S0002-9947-00-02404-1
PII:
S 0002-9947(00)02404-1
Keywords:
Inflection point,
height function,
asymptotic direction
Received by editor(s):
September 29, 1997
Received by editor(s) in revised form:
June 15, 1998
Posted:
March 15, 2000
Additional Notes:
Research of the first author was partially supported by CNPq and FUNAPE, Brazil.
Research of the third author was partially supported by DGCYT, grant no. PB96-0785
Research of the fourth author was partially supported by CNPq, Brazil, grant # 300066/88-0.
Copyright of article:
Copyright
2000,
American Mathematical Society
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