Estudo comparativo do efeito da criopreservação sobre as propriedades biológicas d...
- Auxílios pontuais (curta duração)
Texto completo | |
Autor(es): |
Número total de Autores: 2
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Afiliação do(s) autor(es): | [1] Iwate Med Univ, Ctr Liberal Arts & Sci, Dept Informat Sci, 2-1-1 Nishitokuda, Yahaba Cho, Yahaba, Iwate 0283694 - Japan
[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Ave Trabalhador Sao Carlense, 400 Ctr, BR-13566590 Sao Carlos, SP - Brazil
Número total de Afiliações: 2
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Tipo de documento: | Artigo Científico |
Fonte: | BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY; v. 48, n. 4, p. 679-696, DEC 2017. |
Citações Web of Science: | 0 |
Resumo | |
The simplest way to have birth of surfaces is through transitions in the fibres of a function f with a Morse singularity of index 0 or 3. It is natural to seek to understand the geometry of newly born surfaces. We consider here the question of finding how many umbilics are on a newly born surface. We show that newly born surfaces in the Euclidean 3-space have exactly 4 umbilic points all of type lemon, provided that the Hessian of f at the singular point has pairwise distinct eigenvalues. This is true in both cases when f is an analytic or a smooth germ. When only two of such eigenvalues are equal, the number of umbilic points is either 2, 4, 6 or 8 when f is an analytic or a generic smooth germ. The same results holds for newly born surfaces in the Minkowski 3-space. In that case when the two eigenvalues associated to the two spacelike eigenvectors are distinct we get exactly 4 umbilic points all of type lemon. If they are equal, the number of umbilic points is either 2, 4, 6 or 8. (AU) | |
Processo FAPESP: | 16/02701-4 - Teroria das singularidades plana e redonda |
Beneficiário: | Farid Tari |
Linha de fomento: | Bolsas no Exterior - Pesquisa |
Processo FAPESP: | 14/00304-2 - Singularidades de aplicações diferenciáveis: teoria e aplicações |
Beneficiário: | Maria Aparecida Soares Ruas |
Linha de fomento: | Auxílio à Pesquisa - Temático |
Processo FAPESP: | 13/02543-1 - A geometria de superfícies singulares de ponto de vista da teoria das singularidades |
Beneficiário: | Hasegawa Masaru |
Linha de fomento: | Bolsas no Brasil - Pós-Doutorado |