SITO NON PIU' AGGIORNATO - UNIVERSITÀ DI PAVIA

Dipartimento di Matematica ''F. Casorati''

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Differential and Complex Geometry

Professors:
Bonsante Francesco
Year:
2017/2018
Course code:
504309
ECTS:
9
SSD:
MAT/03
DM:
270/04
Lessons:
72
Period:
I semester
Language:
Italian

Objectives

The course is an introduction to the basic concepts and methods of differential geometry.

Teaching methods

Lectures

Examination

Oral Exam

Prerequisites

The contents of the courses Algebra 1, Geometry 1 and 2, Linear Algebra, and of the courses in Analysis of the Laurea in Mathematics curriculum.

Syllabus

Differentiable manifolds: tangent and cotangent spaces, vector fields and differential forms, vector fields and coordinates: the Frobenius theorem, Lie groups and Lie algebras.
Topics in differential topology: Sard’s lemma, the deRham theorem.
Riemannian geometry: Riemannian manifolds and Levi-Civita connections, curvature, geodesics, completeness, the theorems of Hopf-Rinow and Whitehead; Jacobi fields.
Complex manifolds (if time allows): holomorphic functions of several complex variables and their basic properties, meromorphic functions, complex manifolds, Kähler manifolds.

Bibliography

Notes by Gian Pietro Pirola.
Frank Warner: "Foundations of differentiable manifolds and Lie groups". Graduate Texts in Mathematics, 94. Springer-Verlag, New York-Berlin.
Manfredo Perdigao Do Carmo: "Riemannian Geometry", Birkhaeuser.
Boothby, William M.: "An introduction to differentiable manifolds and Riemannian geometry". Pure and Applied Mathematics, No. 63. Academic Press, New York-London, 1975.
Th. Broecker and K. Jaenich: "Introduction to differential topology".
Milnor, J.: "Morse theory". Annals of Mathematics Studies, No. 51 Princeton University Press, Princeton, N.J. 1963.
D. Huybrechts: "Complex geometry. An introduction". Universitext. Springer-Verlag, Berlin, 2005.



Dipartimento di Matematica ''F. Casorati''

Università degli Studi di Pavia - Via Ferrata, 5 - 27100 Pavia
Tel +39.0382.985600 - Fax +39.0382.985602