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The geometry of singular surfaces from the singularity theory viewpoint

Grant number: 13/02543-1
Support Opportunities:Scholarships in Brazil - Post-Doctoral
Start date: October 01, 2013
End date: February 29, 2016
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Farid Tari
Grantee:Hasegawa Masaru
Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

There is a growing interest in applying singularity theory to the geometry of singular submanifolds in R^n. There are several reasons for this. One of them is that some singularities of these objects are stable, and another is that the singular submanifolds in question may originate from a smooth submanifold M. For example, the wave-fronts (parallels) and the caustic associated to a given smooth sub-manifold in R^n can have stable singularities. The geometry of the frontes and caustics do reveal rich geometric information about the original smooth submanifold M itself. We propose to study the geometry of parameterized surfaces in R^3 with A-simple singularities as well as the geometry of the fibres of functions with simple R-singularities.

News published in Agência FAPESP Newsletter about the scholarship:
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Scientific publications (4)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
FUKUI, TOSHIZUMI; HASEGAWA, MASARU; NAKAGAWA, KOUICHI. Contact of a regular surface in Euclidean 3-space with cylinders and cubic binary differential equations. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, v. 69, n. 2, p. 819-847, . (13/02543-1)
HASEGAWA, MASARU; HONDA, ATSUFUMI; NAOKAWA, KOSUKE; SAJI, KENTARO; UMEHARA, MASAAKI; YAMADA, KOTARO. Intrinsic properties of surfaces with singularities. INTERNATIONAL JOURNAL OF MATHEMATICS, v. 26, n. 4, . (13/02543-1)
HASEGAWA, MASARU. PARABOLIC, RIDGE AND SUB-PARABOLIC CURVES ON IMPLICIT SURFACES WITH SINGULARITIES. OSAKA JOURNAL OF MATHEMATICS, v. 54, n. 4, p. 707-721, . (13/02543-1)
HASEGAWA, MASARU; TARI, FARID. On Umbilic Points on Newly Born Surfaces. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 48, n. 4, p. 679-696, . (16/02701-4, 14/00304-2, 13/02543-1)