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Dissection Thread
An important problem in differential geometry is to find a canonical metric on
a given manifold. In turn, the existence of a canonical metric often has profound
topological implications. A good example is the classical uniformization theorem in
two dimensions which, on one hand, provides a complete topological classification for
compact surfaces, and on the other hand shows that every compact surface has a
canonical geometric structure: a metric of constant curvature.
>differential geometry
>canonical metric
>manifold
>classical uniformization theorem
>compact surfaces
How many of you can define these without looking on the internet?
I will run this thread once every week where I would put excertps from top quality papers.
We will wait for that one guy who can dissect excerpts for us.
I don't know this sounds like a fun activity.
>>
you might want to make these threads when you know a little more about what you're posting
asking for the definition of differential geometry is a serious tip-off
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>>8808056
just the definition. Like I and you can define what is probability, what is combinatorics etc.
This is to facilitate anons to follow a top down approach to certain papers.
Question that would arise by looking at Perelman are:
>What is poincare conjucture?
>Which filed of mathematics has this conjecture?
>Do I know this field
>What if I want to learn about this field and how should I direct my studies.
I agree I myself don't know anything about this but the idea is to gather like minded anon and in doing that help each other.
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>>8808053
why you use the genius pic?
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>>8808121
I have been here for almost 1 hour and I feel like
we are way lower in genius level than Prelman and Terence.
How to fix this?
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>>8808316
Easy
>How to Become a Pure Mathematician
http://hbpms.blogspot.pt/
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>>8808053
>differential geometry
There is not really a universal definition. I consider Differential Geometry to be the study of manifolds w/ some type of additional structure induced by a principal/vector bundle.
>canonical metric
This is not a universal term.
>manifold
Paracompact Hausdorff space locally isomorphic to R^n or C^n. Definition of "isomorphic" varying.
>classical uniformization theorem
Don't know.
>compact surfaces
A 2-manifold where every cover has a finite subcover.
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>>8808353
You make realise that I am brainlet.
Thanks
What are you? A topology student?
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>>8808373
Mathematical Physics with a geometric focus.
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>>8808336
Waoh.Are you following this yourself?
This is gold mine.
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>>8808353
By "induced by a principal bundle" do you mean a structure reduction of the frame bundle? This does not include structures given by tensorfields right?
Thread posts: 11
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Thread images: 2