Generic Curve in R^n: What We Know

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Discussion Overview

The discussion revolves around the characteristics of curves in R^n that have constant curvatures κ1, κ2,..., κn-1. Participants explore what can be inferred about such curves, particularly in the context of a homework problem.

Discussion Character

  • Homework-related, Conceptual clarification

Main Points Raised

  • One participant inquires about the nature of curves in R^n given constant curvatures, suggesting a need for a description of these curves.
  • Another participant points out that without specific information about the values of the curvatures, little can be determined about the curves.
  • A participant clarifies that the exercise specifically asks for a description of curves with constant curvatures, indicating a focus on general types of such curves.
  • There is a suggestion that the original poster should use the appropriate homework forum and include the full problem statement along with relevant equations and their own thoughts.
  • Another participant encourages the original poster to conduct some preliminary research, implying that external resources may provide useful insights.
  • The original poster acknowledges the need to follow forum guidelines and expresses intent to repost in the appropriate homework section.

Areas of Agreement / Disagreement

Participants generally agree that the inquiry pertains to a homework problem and that specific details about the curvatures are necessary for a meaningful discussion. However, there is no consensus on the nature of the curves themselves, as the discussion has not yet delved into specific characteristics or examples.

Contextual Notes

The discussion lacks specific values or definitions for the curvatures κ1, κ2,..., κn-1, which limits the ability to draw conclusions about the curves in question. Additionally, there is an emphasis on the need for a complete problem statement and relevant context to facilitate further exploration.

diffgeo4life
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TL;DR
κ1,κ2,...,κn-1 is constant
What do we know of a curve(/what can it look like) in R^n if we know that κ1,κ2,...,κn-1 is constant?
 
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If you don't tell us what the ##\kappa##s are, not a lot.
 
Precisely the exercise asks: "Describe those curves of general type in R^n which have
constant curvatures."
 
So this is a homework type problem then. It should therefore be posted in the appropriate homework forum using the homework template - including the full problem statement, relevant equations, and your work/thoughts so far.
 
Orodruin said:
your work/thoughts so far.
Indeed. @diffgeo4life - a little bit of Googling will get you at least part way there even if your textbook isn't helpful.
 
Orodruin said:
So this is a homework type problem then. It should therefore be posted in the appropriate homework forum using the homework template - including the full problem statement, relevant equations, and your work/thoughts so far.
Sorry then, I guess then i will try posting in the Homework- Calculus and beyond forum, that looks most appropriate
 
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