The Course will treat several standard topics in basic differential geometry, as differentiable manifolds, Riemannian metrics, geodesics, curvature and related theorems, Lie group and Lie algebras theory as well as Lie group actions on manifolds .
F. Warner Foundations of differentiable manifolds and Lie groups. Graduate Texts in Mathematics, 94. Springer-Verlag, 1983.
T. Sakai, Riemannian geometry. Translations of Mathematical Monographs, 149. American Mathematical Society, 1996.
S. Helgason, Differential geometry, Lie groups, and symmetric spaces. Graduate Studies in Mathematics, 34. American Mathematical Society, 2001
Lecture Notes.
Learning Objectives
Knowledge acquired:
Basics in Differential Geometry
Competence acquired:
Basic tools in Differential Geometry.
Skills acquired (at the end of the course):
The student will be able to solve some problems of medium difficulty in a standard basic course in Differential Geometry.
Prerequisites
Courses to be used as requirements (required and/or recommended)
Courses required: none
Courses recommended: none
Teaching Methods
CFU: 9
Total hours of the course (including the time spent in attending lectures, seminars, private study, examinations, etc...): 72
Hours reserved to private study and other indivual formative activities: 102
Hours for lectures: 72
Hours for laboratory: 0
Hours for laboratory-field/practice: 0
Seminars (hours): 0
Stages (hours): 0
Intermediate examinations (hours): 0
Further information
Attendance of lectures, practice and lab:
Not mandatory
Teaching tools:
None
Office hours:
To be announced, upon request by e-mail.
Contact:
V.le Morgagni 67/A
Phone: 055 2055401
Fax: 055 4237165
E-mail: podesta@math.unifi.it
verdiani@math.unifi.it
Type of Assessment
Oral exam
Course program
The course will treat basic arguments in Differential Geometry. In particular:
Differentiable manifolds, tangent spaces, tensor spaces; differential forms. Frobenius Theorem
Riemannian metrics and basic results in Riemannian geometry and curvature.
Lie Groups : basic theorems concerning the classification of Lie groups and algebras. Structure theorems for homogeneous spaces and Lie group actions on manifolds.