prove that parametric curves are lines of curvature iff g12 = L12. [closed]











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Anybody can explain me how to solve this problem of parametric curves .
when i try to solve this problem I know line of curvature are those tangent vector which is eigen vector but one thing that's confuse me ,Is this result is valide when g12=L12=0...so please somebody can explain me both results and give me proof of both result..










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closed as off-topic by MisterRiemann, user302797, s.harp, user10354138, tatan Nov 24 at 19:05


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – MisterRiemann, user302797, s.harp, user10354138, tatan

If this question can be reworded to fit the rules in the help center, please edit the question.













  • Are not the principal parametric lines defined that way?
    – Narasimham
    Nov 24 at 19:10















up vote
0
down vote

favorite












Anybody can explain me how to solve this problem of parametric curves .
when i try to solve this problem I know line of curvature are those tangent vector which is eigen vector but one thing that's confuse me ,Is this result is valide when g12=L12=0...so please somebody can explain me both results and give me proof of both result..










share|cite|improve this question















closed as off-topic by MisterRiemann, user302797, s.harp, user10354138, tatan Nov 24 at 19:05


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – MisterRiemann, user302797, s.harp, user10354138, tatan

If this question can be reworded to fit the rules in the help center, please edit the question.













  • Are not the principal parametric lines defined that way?
    – Narasimham
    Nov 24 at 19:10













up vote
0
down vote

favorite









up vote
0
down vote

favorite











Anybody can explain me how to solve this problem of parametric curves .
when i try to solve this problem I know line of curvature are those tangent vector which is eigen vector but one thing that's confuse me ,Is this result is valide when g12=L12=0...so please somebody can explain me both results and give me proof of both result..










share|cite|improve this question















Anybody can explain me how to solve this problem of parametric curves .
when i try to solve this problem I know line of curvature are those tangent vector which is eigen vector but one thing that's confuse me ,Is this result is valide when g12=L12=0...so please somebody can explain me both results and give me proof of both result..







differential-geometry






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edited Nov 18 at 12:49

























asked Nov 18 at 7:19









Dheeraj

12




12




closed as off-topic by MisterRiemann, user302797, s.harp, user10354138, tatan Nov 24 at 19:05


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – MisterRiemann, user302797, s.harp, user10354138, tatan

If this question can be reworded to fit the rules in the help center, please edit the question.




closed as off-topic by MisterRiemann, user302797, s.harp, user10354138, tatan Nov 24 at 19:05


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – MisterRiemann, user302797, s.harp, user10354138, tatan

If this question can be reworded to fit the rules in the help center, please edit the question.












  • Are not the principal parametric lines defined that way?
    – Narasimham
    Nov 24 at 19:10


















  • Are not the principal parametric lines defined that way?
    – Narasimham
    Nov 24 at 19:10
















Are not the principal parametric lines defined that way?
– Narasimham
Nov 24 at 19:10




Are not the principal parametric lines defined that way?
– Narasimham
Nov 24 at 19:10















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