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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2025/2026

Introduction to Curves and Surfaces 2

The course is not on the list Without time-table
Code Completion Credits Range
02UKP2 Z 2 1P+1C
Course guarantor:
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-Weingartens equations

5. Christoffels symbols

6. Codazzis equation

7. Riemanns and Riccis 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.Christoffels symbols for a plane and a sphere

5. Riemanns 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.Christoffels symbols for a plane and a sphere

5. Riemanns 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 > katedra fyziky > studentský servis > Doprovod přednášek > 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:
Further information:
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2025-04-06
For updated information see http://bilakniha.cvut.cz/en/predmet5965806.html