Riemann Geometry

  • #1
208
20

Main Question or Discussion Point

So I was reading now about the new geometries and I wanted to know if I can study the Reimann Geometry knowing that I finished high school or if I could just know about it but not about the formulas. I am so interested in the subject because it is used in astronomy.
 

Answers and Replies

  • #2
11,500
5,045
You can read about it at Wikipedia:

https://en.wikipedia.org/wiki/Riemannian_geometry

Its a branch of Differential Geometry. To fully understand it you'll need some background in Calculus, Linear Algebra, Differential Equations and Vector/Tensor Analysis.
 
  • #3
208
20
You can read about it at Wikipedia:

https://en.wikipedia.org/wiki/Riemannian_geometry

Its a branch of Differential Geometry. To fully understand it you'll need some background in Calculus, Linear Algebra, Differential Equations and Vector/Tensor Analysis.
Can u advice me of any track to go with to learn it ? Books , textbooks ...
 
  • #4
11,500
5,045
To get an understanding of some of the topics study the videos at:

www.MathIsPower4U.com

They cover topics from HS to Calculus I II and III,Linear Algebra and Differential Equations and some Vector Analysis in Calculus III.

For the other stuff you'll need textbooks. However the MIT Online Courses may cover Tensor Analysis and Differential Forms and even Differential Geometry itself.

Here's some of the Differential Geometry courses they have:

http://search.mit.edu/search?site=ocw&client=mit&getfields=*&output=xml_no_dtd&proxystylesheet=http://ocw.mit.edu/search/google-ocw.xsl&requiredfields=WT%2Ecg_s:Course+Home|WT%2Ecg_s:Resource+Home&sectionlimit=WT%2Ecg_s:Course+Home|WT%2Ecg_s:Resource+Home&as_dt=i&oe=utf-8&departmentName=web&filter=0&courseName=&q=differential+geometry&btnG.x=0&btnG.y=0

I'll leave it to you to search the site for the others I mentioned earlier.
 
  • #5
208
20
To get an understanding of some of the topics study the videos at:

www.MathIsPower4U.com

They cover topics from HS to Calculus I II and III,Linear Algebra and Differential Equations and some Vector Analysis in Calculus III.

For the other stuff you'll need textbooks. However the MIT Online Courses may cover Tensor Analysis and Differential Forms and even Differential Geometry itself.

Here's some of the Differential Geometry courses they have:

http://search.mit.edu/search?site=ocw&client=mit&getfields=*&output=xml_no_dtd&proxystylesheet=http://ocw.mit.edu/search/google-ocw.xsl&requiredfields=WT%2Ecg_s:Course+Home|WT%2Ecg_s:Resource+Home&sectionlimit=WT%2Ecg_s:Course+Home|WT%2Ecg_s:Resource+Home&as_dt=i&oe=utf-8&departmentName=web&filter=0&courseName=&q=differential+geometry&btnG.x=0&btnG.y=0

I'll leave it to you to search the site for the others I mentioned earlier.
Thank you very much sir
 
  • #6
chiro
Science Advisor
4,790
131
Hey jamalkoiyess.

Riemannian geometry is basically looking at geometry where the different components (like axis, basis vectors, etc) are dependent.

This means that instead of different pieces of information being independent (where you change one piece of information and the others stay the same), they are dependent (meaning you change one piece of information and it will - in some case change something else).

That is the intuition behind differential and Riemannian geometry. It just means that instead of the information in each co-ordinate (or basis vector) being independent, they relate to each other in some way.

Things like space-time have this property where if you change one thing then it changes the kinds of values that the other should have.

It used to be that people thought that the best way to understand things was through independence - but eventually a few mathematicians realized that it might be a good idea to look past that and it's applications have been used extensively (including in the well known use of General Relativity).
 
  • #7
208
20
Hey jamalkoiyess.

Riemannian geometry is basically looking at geometry where the different components (like axis, basis vectors, etc) are dependent.

This means that instead of different pieces of information being independent (where you change one piece of information and the others stay the same), they are dependent (meaning you change one piece of information and it will - in some case change something else).

That is the intuition behind differential and Riemannian geometry. It just means that instead of the information in each co-ordinate (or basis vector) being independent, they relate to each other in some way.

Things like space-time have this property where if you change one thing then it changes the kinds of values that the other should have.

It used to be that people thought that the best way to understand things was through independence - but eventually a few mathematicians realized that it might be a good idea to look past that and it's applications have been used extensively (including in the well known use of General Relativity).
Thank you very much for the detailed explanation sir. I will look a little further and buy myself some textbooks
 

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