Differential Geometry

Code:

M3007

Acronym:

M3007

Level:

300

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2016/2017 - 2S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:B	0	Official Study Plan	3	-	6	56	162
L:M	7	Official Study Plan	2	-	6	56	162
			3
L:Q	3	study plan from 2016/17	3	-	6	56	162

Teaching language

Suitable for English-speaking students

Objectives

Introduce the students to the local and global properties of manifolds in euclidean space. Presentation of the basic concepts of riemannian geometry.

Learning outcomes and competences

At the end of the course the student should have the necessary basis to attend a course on abstract Differentiable Manifolds, including Riemannian Manifolds, presented with the modern formalisms.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Multivariable Calculus. Linear and Multilinear Algebra.

Program

Manifolds in R^n: Tangent space. Diferentiables mappings between manifolds. Cotangent space. The differential. Vector fields and co-vector fields. Riemannian manifolds. The metric tensor. First fundamental form. Christoffel symbols. Covariant derivatives. The Levi-Civita connexion. Geodesics. Geidesic curvatura. The second fundamental form. Pricipal curvatures. The curvature tensor.

Mandatory literature

Banchoff Thomas F.; Differential geometry of curves and surfaces. ISBN: 978-1-56881-456-8

Complementary Bibliography

Kuhnel Wolfgang; Differential geometry. ISBN: 0-8218-2656-5
Carmo Manfredo Perdigão do 675; Geometria diferencial de curvas e superfícies. ISBN: 9788585818265

Teaching methods and learning activities

Classroom presentation of the theory and resolution of exercises

keywords

Physical sciences > Mathematics > Geometry

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	70,00
Participação presencial	5,00
Trabalho escrito	25,00
Total:	100,00

Calculation formula of final grade

FG - grade in the final exam
CP - grade for classroom participation
AE - grade (average) for the assignments or projects

0,70*FG+0,05*CP+0,25*AE