The Morse lemma and applications.

• Grant number: 08/09845-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2009
• End date: November 30, 2010
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Eliris Cristina Rizziolli
• Grantee: Pedro Gomes Teixeira
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil

Abstract

This work will deal with important results in Singulariry Theory: the Morse Lemma, as well as, Morse lemma with parameters. For this purpose, we will study: the differential geometry to the plane curves and space curves, the smooth maps from $\mathbb{R}^n$ to$\mathbb{R}$, the right equivalence, jets, regular values and tangent spaces. Besides, we will examine some examples.