Course Title: |
**Euclidean Curves & Surfaces** |

Course Number: |
MATH 4530 - 1 |

Instructor: |
Andrejs Treibergs |

Days: |
M, W, F, 10:45 - 11:35 AM in *LCB 215* |

Office Hours: |
12:40-1:30 M, W, F, in JWB 224 (tent.) |

E-mail: |
`treiberg@math.utah.edu` |

Prerequisites: |
Advanced calculus
(e.g. MATH 2210 or consent of instructor.) |

Text: |
John Oprea, *Differential Geometry, 2nd. ed.* PEARSON/Prentice Hall, 2004. |

# Final for M 4530-1 is Monday, May 3, 2004 at 10:30 am - 12:30 pm in LCB 215.

# Supplementary Notes for M4530

`http://www.math.utah.edu/~treiberg/M4530.ps`,
`.pdf`
`http://www.math.utah.edu/~treiberg/M4530b.ps`,
`.pdf`,
`.dvi`

MAPLE worksheet for reviewing of M4530

`http://www.math.utah.edu/~treiberg/M4530.mws`

## The Hyperbolic Plane and its Immersions into *R*^{3}

We study how to describe and compute geometric features of curved surfaces in Euclidean three space.
We describe the Gauß and mean curvature of a surface. We shall discuss applications to cartography,
soap films and bubbles. We shall touch opun mechanical and variational principles.
We shall also mention non-Euclidean geometries. We shall use the MAPLE computer algebra system to illustrate text and lectures.

Topics include (depending on time):

- Curves in the plane and in three space.
- Isoperimetric Inequality.
- Differentiating functions and vector fields on a surface.
- Normal curvature of curves on a surface.
- Gauß curvature Surfaces of revolutiuon.
- Minimal surfaces. Conformal maps. Mercator projection.
- Constant Mean Curvature Surfaces.
- Isometric Immersions. Second fundamental form.
- Complete manifolds. Geodesics.
- Gauß Bonnet Theorem.
- Hilbert's theorems on immersing the sphere and the hyperbolc plane.

Last updated: 3 / 26 / 4