CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

# Introduction to Curves and Surfaces 2

Code Completion Credits Range
02UKP2 Z 2 1P+1C
Lecturer:
Tutor:
Supervisor:
Department of Physics
Synopsis:

The lecture extends the course 02UKP1. The properties of the first fundamental form are briefly summarized. The concept of the second fundamental form is introduced, leading to the mean and Gaussian curvature. Finally, the usual concepts of Riemann geometry are introduced.

Requirements:
Syllabus of lectures:

Outline of the lecture:

1. First fundamental form – review

2. Second fundamental form

3. Mean and Gaussian curvature of a surface

4. Gauss-Weingarten‘s equations

5. Christoffel‘s symbols

6. Codazzi’s equation

7. Riemann‘s and Ricci’s tensor of curvature

8. Gauss theorema egregium

Outline of the exercises:

1.Metrix tensor of a sphere and torus.

2.Evaluation of the mean and Gaussian curvature with the second fundamental

3.Surfaces with zero mean and zero Gaussian curvature

4.Christoffel’s symbols for a plane and a sphere

5. Riemann’s tensor for a plane and a sphere

Syllabus of tutorials:

Outline of the exercises:

1.Metrix tensor of a sphere and torus.

2.Evaluation of the mean and Gaussian curvature with the second fundamental

3.Surfaces with zero mean and zero Gaussian curvature

4.Christoffel’s symbols for a plane and a sphere

5. Riemann’s tensor for a plane and a sphere

Study Objective:

Knowledge:

To provide the simplest examples of manifolds and their properties.

Acquired skills:

Solve mathematical problems defined on manifolds.

Study materials:

Key references:

[1] L. Hlavatý, Úvod do křivek a ploch (in Czech)

www.fjfi.cvut.cz &gt; katedra fyziky &gt; studentský servis &gt; Doprovod přednášek &gt; Úvod do křivek a ploch

Recommended references:

[2] B. Hostinský, Diferenciální geometrie křivek a ploch, Přírodovědecké nakladatelství v Praze, 1949 (in Czech)

[3] W. Kuehnel, Diferential Geometry, AMS2006

[4] T. Banchoff, S Lovett , Diferential Geometry of Curves and Surfaces, CRC Press 2016

Note:
Time-table for winter semester 2019/2020:
Time-table is not available yet
Time-table for summer semester 2019/2020:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2020-01-19
For updated information see http://bilakniha.cvut.cz/en/predmet5965806.html