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0

$begingroup$

I am trying to understand Differential Geometry and I am not able to understand why we define vectors in it, a certain way as operators.

The textbooks mention that writing it as directional derivatives gives us a coordinate free way to define the vector.

So are the values in spherical polar and cartesian same?

multivariable-calculus differential-geometry

share|cite|improve this question

edited yesterday

Ted Shifrin

64.2k44692

asked yesterday

Chetan WaghelaChetan Waghela

688

$endgroup$

add a comment | 

0

$begingroup$

I am trying to understand Differential Geometry and I am not able to understand why we define vectors in it, a certain way as operators.

The textbooks mention that writing it as directional derivatives gives us a coordinate free way to define the vector.

So are the values in spherical polar and cartesian same?

multivariable-calculus differential-geometry

share|cite|improve this question

edited yesterday

Ted Shifrin

64.2k44692

asked yesterday

Chetan WaghelaChetan Waghela

688

$endgroup$

add a comment | 

$begingroup$

I am trying to understand Differential Geometry and I am not able to understand why we define vectors in it, a certain way as operators.

The textbooks mention that writing it as directional derivatives gives us a coordinate free way to define the vector.

So are the values in spherical polar and cartesian same?

multivariable-calculus differential-geometry

share|cite|improve this question

edited yesterday

Ted Shifrin

64.2k44692

asked yesterday

Chetan WaghelaChetan Waghela

688

$endgroup$

share|cite|improve this question

edited yesterday

Ted Shifrin

64.2k44692

asked yesterday

Chetan WaghelaChetan Waghela

688

share|cite|improve this question

edited yesterday

Ted Shifrin

64.2k44692

asked yesterday

Chetan WaghelaChetan Waghela

688

edited yesterday

Ted Shifrin

64.2k44692

edited yesterday

Ted Shifrin

64.2k44692

asked yesterday

Chetan WaghelaChetan Waghela

688

asked yesterday

Chetan WaghelaChetan Waghela

688