# Questions tagged [differential-geometry]

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### Length of a toroidal helix

For the toroidal helix defined by ...
1 vote
34 views

### Integrate Differential Form with Parameter with DifferentialForms.m?

In this post, it is shown how to integrate a function with parameter(s) and output a function of the parameter(s). I am trying to do something similar with the DifferentialForms.m package. I have ...
23 views

### HomotopyOperator in DifferentialForms.m Not Working

I'm trying to implement and check Faraday's tensor with the DifferentialForms.m package. I code this to implement the Faraday 2-form ...
154 views

92 views

### Problem with ArcCurvature

When comparing the outputs of ...
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240 views

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240 views

### A doubt on ParametricPlot3D, RevolutionPlot3D, ListPlots and NIntegrate: can I build an "RevolutionListPlot3D"?

First of all: this is question lies in the context of Surfaces and Embbedings on differential geometry. More precisely in the context of Kruskal coordinates and how to plot a 3D dynamical ...
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358 views

### Why do isolated large values of WorkingPrecision fail in NDSolve?

Executive Summary: Getting an accurate answer often depends on setting the WorkingPrecision high enough. Once it is high enough, though, I would expect that its ...
• 531
1 vote
89 views

### Problem with the analytical study of transient processes in nonlinear systems with linear dynamic links

I ask for advice and help. I am having difficulties of this nature. There is a nonlinear system of the following type: I need to analyze analytically the transient process in such a system. The ...
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1 vote
129 views

### DSolve does not work

I am trying to solve this coupled nonlinear pdes for $\kappa(x,t)$ and $\tau(x,t)$: where $\zeta_1 = \kappa(x,t)$, $\zeta_2 = 0$. I used this code ...
453 views

### Coordinate-free derivative

Given the function \begin{align*} f \colon \mathbb{R}^n &\to \mathbb{R}^n\\ v&\mapsto \dfrac{v}{\|v\|}, \end{align*} I would like to compute the derivative of $f$, that is $df(v)$. It is ...
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1 vote
158 views

### Cannot derive Norm or Normalize when recreating Frenet Serret equations

I'm trying to calculate the torsion of a curve at a point using the following code: ...
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1 vote
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### How Can I draw a curve on a sphere in Minkowski 3 space?

There is a curve, which evolves with time, in the the Euclidean space. And the solution of its evolution equations has been used to draw it using this code: ...
410 views

### How is Grad defined for array particularly in non-Cartesian coordinates?

This question can be viewed as a follow-up of What is the definition of Curl in Mathematica? First argument of Grad can be an array, but what definition does ...
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179 views

### How to identify specific Christoffel symbols and Riemann Tensor components from a general solution [closed]

I want to learn how to identify specific Christoffel Symbols and Riemman Tensor components from the general solution provided by Mathematica. Let us work out an example to see what I mean clearly. ...
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