Find the values $omega_{X}(v)$ of the $1$-forms of $omega$ at all possible locations $X$ and directions $V$
I just started reading from a differential forms book, and I've been struggling with the following problem:
Find the values $omega_{X}(v)$ of the $1$-forms of $omega$ at all
possible locations $X$ and directions $V$ for
$$omega = (y^2 - x^2)mathop{dx} + y^2 mathop{dy} + zmathop{dx} + y
mathop{dy} - xy^{2} mathop{dz}$$
for $X = (2,3),(3,5),(1,-1),(2,3,4)$ and $V = (3,-7,1),(4,5),(-2,1)$.
I really have no idea how to stat this problem, and the book doesn't have many examples similar to it. I was wondering if someone could please explain the answer to me in a slow way for someone new to this type of thing.
derivatives differential-geometry differential-forms
asked Nov 30 '18 at 1:54
josephjoseph
4329
add a comment |
I just started reading from a differential forms book, and I've been struggling with the following problem:
Find the values $omega_{X}(v)$ of the $1$-forms of $omega$ at all
possible locations $X$ and directions $V$ for
$$omega = (y^2 - x^2)mathop{dx} + y^2 mathop{dy} + zmathop{dx} + y
mathop{dy} - xy^{2} mathop{dz}$$
for $X = (2,3),(3,5),(1,-1),(2,3,4)$ and $V = (3,-7,1),(4,5),(-2,1)$.
I really have no idea how to stat this problem, and the book doesn't have many examples similar to it. I was wondering if someone could please explain the answer to me in a slow way for someone new to this type of thing.
derivatives differential-geometry differential-forms
asked Nov 30 '18 at 1:54
josephjoseph
4329
So $omega$ is a $1$-form on $mathbb{R}^3$. But you have points $x$ given in both $mathbb{R}^2$ and $mathbb{R}^3$. Similarly for your tangent vector $V$. If everything is given on the same manifold (e.g., $mathbb{R}^3$), it would be simple enough, but without that what you have makes no sense.
– Matt
Nov 30 '18 at 12:44
This is all of the information I was given. I just rechecked and I typed the problem correctly. The problem is ranked as 'Easy' though so I don't think it's super complicated
– joseph
Nov 30 '18 at 15:03
I don't know if it helps, but I think I'm supposed to match the $mathbb{R}^{2}$ and $mathbb{R}^{3}$ points to the $1$ form that fits it
– joseph
Nov 30 '18 at 17:05
add a comment |
I just started reading from a differential forms book, and I've been struggling with the following problem:
Find the values $omega_{X}(v)$ of the $1$-forms of $omega$ at all
possible locations $X$ and directions $V$ for
$$omega = (y^2 - x^2)mathop{dx} + y^2 mathop{dy} + zmathop{dx} + y
mathop{dy} - xy^{2} mathop{dz}$$
for $X = (2,3),(3,5),(1,-1),(2,3,4)$ and $V = (3,-7,1),(4,5),(-2,1)$.
I really have no idea how to stat this problem, and the book doesn't have many examples similar to it. I was wondering if someone could please explain the answer to me in a slow way for someone new to this type of thing.
derivatives differential-geometry differential-forms
asked Nov 30 '18 at 1:54
josephjoseph
4329
I just started reading from a differential forms book, and I've been struggling with the following problem:
Find the values $omega_{X}(v)$ of the $1$-forms of $omega$ at all
possible locations $X$ and directions $V$ for
$$omega = (y^2 - x^2)mathop{dx} + y^2 mathop{dy} + zmathop{dx} + y
mathop{dy} - xy^{2} mathop{dz}$$
for $X = (2,3),(3,5),(1,-1),(2,3,4)$ and $V = (3,-7,1),(4,5),(-2,1)$.
I really have no idea how to stat this problem, and the book doesn't have many examples similar to it. I was wondering if someone could please explain the answer to me in a slow way for someone new to this type of thing.
derivatives differential-geometry differential-forms
derivatives differential-geometry differential-forms
asked Nov 30 '18 at 1:54
josephjoseph
4329
asked Nov 30 '18 at 1:54
josephjoseph
4329
asked Nov 30 '18 at 1:54
josephjoseph
4329
asked Nov 30 '18 at 1:54
josephjoseph
4329
asked Nov 30 '18 at 1:54
josephjoseph
4329
4329
So $omega$ is a $1$-form on $mathbb{R}^3$. But you have points $x$ given in both $mathbb{R}^2$ and $mathbb{R}^3$. Similarly for your tangent vector $V$. If everything is given on the same manifold (e.g., $mathbb{R}^3$), it would be simple enough, but without that what you have makes no sense.
– Matt
Nov 30 '18 at 12:44
This is all of the information I was given. I just rechecked and I typed the problem correctly. The problem is ranked as 'Easy' though so I don't think it's super complicated
– joseph
Nov 30 '18 at 15:03
I don't know if it helps, but I think I'm supposed to match the $mathbb{R}^{2}$ and $mathbb{R}^{3}$ points to the $1$ form that fits it
– joseph
Nov 30 '18 at 17:05
add a comment |
So $omega$ is a $1$-form on $mathbb{R}^3$. But you have points $x$ given in both $mathbb{R}^2$ and $mathbb{R}^3$. Similarly for your tangent vector $V$. If everything is given on the same manifold (e.g., $mathbb{R}^3$), it would be simple enough, but without that what you have makes no sense.
– Matt
Nov 30 '18 at 12:44
This is all of the information I was given. I just rechecked and I typed the problem correctly. The problem is ranked as 'Easy' though so I don't think it's super complicated
– joseph
Nov 30 '18 at 15:03
I don't know if it helps, but I think I'm supposed to match the $mathbb{R}^{2}$ and $mathbb{R}^{3}$ points to the $1$ form that fits it
– joseph
Nov 30 '18 at 17:05
So $omega$ is a $1$-form on $mathbb{R}^3$. But you have points $x$ given in both $mathbb{R}^2$ and $mathbb{R}^3$. Similarly for your tangent vector $V$. If everything is given on the same manifold (e.g., $mathbb{R}^3$), it would be simple enough, but without that what you have makes no sense.
– Matt
Nov 30 '18 at 12:44
So $omega$ is a $1$-form on $mathbb{R}^3$. But you have points $x$ given in both $mathbb{R}^2$ and $mathbb{R}^3$. Similarly for your tangent vector $V$. If everything is given on the same manifold (e.g., $mathbb{R}^3$), it would be simple enough, but without that what you have makes no sense.
– Matt
Nov 30 '18 at 12:44
This is all of the information I was given. I just rechecked and I typed the problem correctly. The problem is ranked as 'Easy' though so I don't think it's super complicated
– joseph
Nov 30 '18 at 15:03
This is all of the information I was given. I just rechecked and I typed the problem correctly. The problem is ranked as 'Easy' though so I don't think it's super complicated
– joseph
Nov 30 '18 at 15:03
I don't know if it helps, but I think I'm supposed to match the $mathbb{R}^{2}$ and $mathbb{R}^{3}$ points to the $1$ form that fits it
– joseph
Nov 30 '18 at 17:05
I don't know if it helps, but I think I'm supposed to match the $mathbb{R}^{2}$ and $mathbb{R}^{3}$ points to the $1$ form that fits it
– joseph
Nov 30 '18 at 17:05
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%2f3019515%2ffind-the-values-omega-xv-of-the-1-forms-of-omega-at-all-possible-loc%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.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- 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.
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%2f3019515%2ffind-the-values-omega-xv-of-the-1-forms-of-omega-at-all-possible-loc%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
So $omega$ is a $1$-form on $mathbb{R}^3$. But you have points $x$ given in both $mathbb{R}^2$ and $mathbb{R}^3$. Similarly for your tangent vector $V$. If everything is given on the same manifold (e.g., $mathbb{R}^3$), it would be simple enough, but without that what you have makes no sense.
– Matt
Nov 30 '18 at 12:44
This is all of the information I was given. I just rechecked and I typed the problem correctly. The problem is ranked as 'Easy' though so I don't think it's super complicated
– joseph
Nov 30 '18 at 15:03
I don't know if it helps, but I think I'm supposed to match the $mathbb{R}^{2}$ and $mathbb{R}^{3}$ points to the $1$ form that fits it
– joseph
Nov 30 '18 at 17:05