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Differential Geometry III

This class was created by Brainscape user Daisy Smith. Visit their profile to learn more about the creator.

By: Daisy Smith
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Decks in this class (12)

1: Motivation
Four vertex theorem
1  cards
2: Regular Curve
Image alpha i is the ___ of the c...,
Alpha is ___ at u id alpha u 0,
If alpha is regular and norm alph...
6  cards
3: Plane Curves
If alpha smooth unit speed curve ...,
Jordon curve theorem a simple clo...,
If e is___ then its tangent vecto...
4  cards
4: Space Curves
K s measures the rate at which al...,
Torsion measures the rate at whic...,
If alpha is regular and k u 0 and...
4  cards
6: Intro to Surfaces in R3
C is a regular value of f is all ...,
C is called a ___ of f is the pre...,
If u is open and f is smooth and ...
4  cards
7: Tangent Planes, Angles, Lengths, Areas
Tangent plane at p consists of al...,
The tangent space at p does not d...,
Area does not depend on choice of...
3  cards
8: Smooth Maps Between Surfaces
Smoothness of f does not depend o...,
A ___ of the surface is a smooth ...,
A gauss map of a regular surface ...
6  cards
9: Geometry of the Gauss Map
The weingarten map is ___,
X u v is ___ if f 0 fff,
X u v is ___ if f 0 fff and m 0 sff
9  cards
10: Theorema Egregium of Gauss
K depends on e f g and their ___ ...,
A local isometry preserves ___ cu...,
Christoffel symbols are completel...
4  cards
11: Curves on Surfaces
If x is a ___ parametrisation of ...,
If x is a principal parametrisati...,
A curve on a regular surface is c...
4  cards
12: Geodesics
If alpha is a geodesic then norm ...
1  cards
13: Theorem of Gauss-Bonnet
A triangulation of a region is a ...
1  cards

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Differential Geometry III

  • Class purpose General learning

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