| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [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
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY; v. 48, n. 4, p. 679-696, DEC 2017. |
| Web of Science Citations: | 0 |
| Abstract | |
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) | |
| FAPESP's process: | 16/02701-4 - Flat and round singularity theory |
| Grantee: | Farid Tari |
| Support Opportunities: | Scholarships abroad - Research |
| FAPESP's process: | 14/00304-2 - Singularities of differentiable mappings: theory and applications |
| Grantee: | Maria Aparecida Soares Ruas |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 13/02543-1 - The geometry of singular surfaces from the singularity theory viewpoint |
| Grantee: | Hasegawa Masaru |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |