Geometry of singular surfaces in Euclidean space

• Grant number: 18/19610-7
• Support Opportunities: Regular Research Grants
• Start date: December 01, 2018
• End date: November 30, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Luciana de Fátima Martins
• Grantee: Luciana de Fátima Martins
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil

Abstract

The Singularity Theory deals with the study of singular varieties and applications. Due to its wide applications to various areas of science and to its interaction with several areas of Mathematics, Singularity Theory has consolidated and gained great interest from the academic community.The central theme of this project is devoted to the study of the differential geometry of singular surfaces in the Euclidean 3- space $\mathbb{R}^3$, using Singularity Theory techniques, and to the retrieval of properties of regular surfaces that are obtained from properties of singular surfaces associated with them.Singular surfaces can be considered from different points of view and their study is a subject that is developing every day. The present project aims to continue the work we have developed on the subject. We will consider current problems and have aroused interest to several researchers, aiming to contribute significantly to the Singularity Theory itself and its applications to the geometry of singular surfaces.We will consider surfaces given by different aspects, such as those arising from the rotation of a singular plane curve, focal surfaces of singular rotation surfaces, special types of cuspidal edges, screw motion surfaces generated by a singular curve, among others, searching for new invariants and applications, in addition to contributing to studies involving the Poincare Conjecture. The proposed problems will be studied joint with Prof. Kentaro Saji and Keisuke Teramoto, of the University of Kobe, and with Prof. Juan Jose Nuno Ballesteros of the University of Valencia, in addition to my PhD student in Ibilce, Samuel Paulino dos Santos. (AU)

Scientific publications

(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)

MARTINS, LUCIANA F.; SAJI, KENTARO; TERAMOTO, KEISUKE. Singularities of a surface given by Kenmotsu-type formula in Euclidean three-space. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, v. 13, n. 2, p. 663-677, DEC 2019. (18/19610-7)

COSTA, J. C. F.; MARTINS, L. F.; NUNO-BALLESTEROS, J. J.. ON THE INDEX OF PRINCIPAL FOLIATIONS OF SURFACES IN R-3 WITH CORANK 1 SINGULARITIES. JOURNAL OF SINGULARITIES, v. 22, p. 16-pg., 2020-01-01. (18/19610-7, 18/25157-3)

MARTINS LUCIANA F.; KENTARO SAJI; SAMUEL P. DOS SANTOS; KEISUKE TERAMOTO. Singular surfaces of revolution with prescribed unbounded mean curvature. Anais da Academia Brasileira de Ciências, v. 91, n. 3, 2019-09-02. (16/21226-5, 18/17712-7, 18/19610-7)