1
vote
2answers
76 views

Elliptic Curve and Conjugation

If I consider an elliptic curve $C$ as a Riemann surface cut out in $\mathbb{C}P^2$ by a homogenous cubic, and if that cubic is defined over $\mathbb{R}$, then I think we have a conjugation map ...
1
vote
1answer
118 views

Does a Möbius strip have only one shape? Or may it have different shapes?

I'm reading a book about geometry, and after thinking and viewing the Möbius strip, I want to know whether the book is right or not. The book says with a little description (that I can't write here ...
3
votes
1answer
168 views

Visualization of the diffeomorphism!

Basic to all mathematics is the notion-here used quite informally-of a set with structure. For every type of structure there is a notion of equivalence (or isomorphism)-a one-to-one onto ...
1
vote
1answer
58 views

Definition of the punctured $\mathbb{R}P^3$

I faced "punctured $\mathbb{R}P^3$" denoted by $\mathbb{R}P^3-\{{pt}\}$ in my studies. I dont know its definition and also my searches in the web are failed. Can anyone help me? What is the ...
4
votes
0answers
178 views

Visualization of immersed submanifold

I am trying to visualize the difference between immersed submanifold and embedded submanifold. At first, I thought that, for example, if I can embed manifold $M$ in $\mathbb{R}^4$ and if my friend can ...
1
vote
1answer
92 views

Visualizing diffeomorphisms

This is probably a really basic question (hence my asking it here as opposed to MO). In a comment to a question on mathoverflow ...
7
votes
2answers
150 views

An example of a Lie group

I have a trouble learning Lie groups --- I have no canonical example to imagine while thinking of a Lie group. When I imagine a manifold it is usually some kind of a 2D blanket or a circle/curve or a ...
7
votes
1answer
303 views

Visualizing Exterior Derivative

How do you visualize the exterior derivative of differential forms? I imagine differential forms to be some sort of (oriented) line segments, areas, volumes etc. That is if I imagine a two-form, I ...
3
votes
1answer
1k views

How to visualize the Gaussian curvature of a 3D surface?

I have a 3D surface. I want to visualize color-coded Gaussian Curvature. Is there any software (e.g. MATLAB, Mathematica) which can be used for calculating and visualizing the curvature in color code ...
2
votes
1answer
245 views

general (asymmetric) real rank-2 tensor visualization in 3d

I have general rank-2 real tensor in 3d space represented as a 3x3 real matrix $M$ (it is gradient of a vector field). I am writing some code to visualize it in several isolated points, this is what I ...
7
votes
2answers
763 views

How to Visualize points on a high dimensional (>3) Manifold?

Are there any ways to visualize(plot/draw) points on a high dimensional (ex: dimension = 5) manifold?