Generic Curve in R^n: What We Know

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SUMMARY

The discussion centers on the characteristics of curves in R^n with constant curvatures κ1, κ2,...,κn-1. Participants emphasize the necessity of providing specific values for the curvatures to accurately describe the curves. The conversation also highlights the importance of posting homework-related questions in the appropriate forum, specifically the Homework-Calculus and Beyond forum, along with the complete problem statement and relevant equations for better assistance.

PREREQUISITES
  • Understanding of R^n geometry
  • Knowledge of curvature concepts in differential geometry
  • Familiarity with homework posting protocols in online forums
  • Ability to formulate mathematical problems and equations
NEXT STEPS
  • Research the properties of curves in R^n with constant curvature
  • Study differential geometry textbooks for detailed explanations of curvature
  • Explore online resources for posting homework questions effectively
  • Learn about the implications of constant curvature on the shape of curves
USEFUL FOR

Students studying differential geometry, mathematicians interested in the properties of curves, and anyone seeking guidance on effectively posting homework questions in online forums.

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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