Differential Geometry - Lecture 11: Differential Geometry c...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Lecture 11: Differential Geometry c ° Bryan S. Morse, Brigham Young University, 1998–2000 Last modified on February 28, 2000 at 8:45 PM Contents 11.1 Introduction . ............................................. 1 11.1.1 What Differential Geometry Is . ................................ 1 11.1.2 Assumptions of Differentiability . ............................... 2 11.1.3 Normals and Tangent Planes . ................................. 2 11.1.4 Disclaimer. ........................................... 2 11.1.5 Notation. ............................................ 2 11.2 First Derivatives . ........................................... 2 11.2.1 The Gradient . ......................................... 2 11.2.2 First-order Gauge Coordinates . ................................ 3 11.3 Second Derivatives. .......................................... 3 11.3.1 The Hessian. .......................................... 3 11.3.2 Principal Curvatures and Directions. .............................. 4 11.3.3 Second-order Gauge Coordinates. ............................... 4 11.4 Using Principal Curvatures and Directions. ............................. 4 11.4.1 Gaussian Curvature. ...................................... 4 11.4.2 Mean Curvature. ........................................ 4 11.4.3 Laplacian . ........................................... 4 11.4.4 Deviation From Flatness . ................................... 5 11.4.5 Patch Classification. ...................................... 5 11.4.6 Parabolic Points. ........................................ 5 11.4.7 Umbilics. ............................................ 5 11.4.8 Minimal Points . ........................................ 5 11.4.9 Shape Classification. ...................................... 5 11.5 Other Concepts. ............................................ 6 11.5.1 Geodesics. ........................................... 6 11.5.2 Genericity. ........................................... 6 11.6 Applications (Examples). ....................................... 6
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/07/2011 for the course PHYS 101 taught by Professor Aster during the Spring '11 term at East Tennessee State University.

Page1 / 7

Differential Geometry - Lecture 11: Differential Geometry c...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online