Mixing
Worked examples of Lie derivative
$begingroup$
I'm trying to find the Lie derivative of a 2 form $sin(theta)dtheta dphi$ with respect to a vector field given in a differential basis and I think the way to go here is to use Cartan's formula but I'm not sure how to do that. I can't find any worked examples in any differential textbook or online, everything seems to focus on proving identities not performing actual calculations. Can somebody point me to a useful resource?
differential-geometry derivatives
asked Jan 20 at 22:11
user2992309user2992309
132
$endgroup$
migrated from physics.stackexchange.com Jan 21 at 10:30
This question came from our site for active researchers, academics and students of physics.
add a comment |
$begingroup$
I'm trying to find the Lie derivative of a 2 form $sin(theta)dtheta dphi$ with respect to a vector field given in a differential basis and I think the way to go here is to use Cartan's formula but I'm not sure how to do that. I can't find any worked examples in any differential textbook or online, everything seems to focus on proving identities not performing actual calculations. Can somebody point me to a useful resource?
differential-geometry derivatives
asked Jan 20 at 22:11
user2992309user2992309
132
$endgroup$
migrated from physics.stackexchange.com Jan 21 at 10:30
This question came from our site for active researchers, academics and students of physics.
1
$begingroup$
Would Mathematics be a better home for this question?
$endgroup$
– Qmechanic
Jan 20 at 22:18
1
$begingroup$
actually you might be right there
$endgroup$
– user2992309
Jan 20 at 22:20
$begingroup$
Which space are you working in? I need to know if ${dtheta,dphi}$ is a basis of one-forms or not.
$endgroup$
– Gibbs
Jan 31 at 11:11
add a comment |
$begingroup$
I'm trying to find the Lie derivative of a 2 form $sin(theta)dtheta dphi$ with respect to a vector field given in a differential basis and I think the way to go here is to use Cartan's formula but I'm not sure how to do that. I can't find any worked examples in any differential textbook or online, everything seems to focus on proving identities not performing actual calculations. Can somebody point me to a useful resource?
differential-geometry derivatives
asked Jan 20 at 22:11
user2992309user2992309
132
$endgroup$
I'm trying to find the Lie derivative of a 2 form $sin(theta)dtheta dphi$ with respect to a vector field given in a differential basis and I think the way to go here is to use Cartan's formula but I'm not sure how to do that. I can't find any worked examples in any differential textbook or online, everything seems to focus on proving identities not performing actual calculations. Can somebody point me to a useful resource?
differential-geometry derivatives
differential-geometry derivatives
asked Jan 20 at 22:11
user2992309user2992309
132
asked Jan 20 at 22:11
user2992309user2992309
132
asked Jan 20 at 22:11
user2992309user2992309
132
asked Jan 20 at 22:11
user2992309user2992309
132
asked Jan 20 at 22:11
user2992309user2992309
132
132
migrated from physics.stackexchange.com Jan 21 at 10:30
This question came from our site for active researchers, academics and students of physics.
migrated from physics.stackexchange.com Jan 21 at 10:30
This question came from our site for active researchers, academics and students of physics.
1
$begingroup$
Would Mathematics be a better home for this question?
$endgroup$
– Qmechanic
Jan 20 at 22:18
1
$begingroup$
actually you might be right there
$endgroup$
– user2992309
Jan 20 at 22:20
$begingroup$
Which space are you working in? I need to know if ${dtheta,dphi}$ is a basis of one-forms or not.
$endgroup$
– Gibbs
Jan 31 at 11:11
add a comment |
1
$begingroup$
Would Mathematics be a better home for this question?
$endgroup$
– Qmechanic
Jan 20 at 22:18
1
$begingroup$
actually you might be right there
$endgroup$
– user2992309
Jan 20 at 22:20
$begingroup$
Which space are you working in? I need to know if ${dtheta,dphi}$ is a basis of one-forms or not.
$endgroup$
– Gibbs
Jan 31 at 11:11
1
1
$begingroup$
Would Mathematics be a better home for this question?
$endgroup$
– Qmechanic
Jan 20 at 22:18
$begingroup$
Would Mathematics be a better home for this question?
$endgroup$
– Qmechanic
Jan 20 at 22:18
1
1
$begingroup$
actually you might be right there
$endgroup$
– user2992309
Jan 20 at 22:20
$begingroup$
actually you might be right there
$endgroup$
– user2992309
Jan 20 at 22:20
$begingroup$
Which space are you working in? I need to know if ${dtheta,dphi}$ is a basis of one-forms or not.
$endgroup$
– Gibbs
Jan 31 at 11:11
$begingroup$
Which space are you working in? I need to know if ${dtheta,dphi}$ is a basis of one-forms or not.
$endgroup$
– Gibbs
Jan 31 at 11:11
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3081720%2fworked-examples-of-lie-derivative%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3081720%2fworked-examples-of-lie-derivative%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
$begingroup$
Would Mathematics be a better home for this question?
$endgroup$
– Qmechanic
Jan 20 at 22:18
1
$begingroup$
actually you might be right there
$endgroup$
– user2992309
Jan 20 at 22:20
$begingroup$
Which space are you working in? I need to know if ${dtheta,dphi}$ is a basis of one-forms or not.
$endgroup$
– Gibbs
Jan 31 at 11:11