Mixing
Local tubular neighborhood
$begingroup$
Let $MsubsetBbb R^n$ be a $C^1$ manifold. I need to prove that for any $xin M$, there exist $epsilon>0$ and a neighborhood $V$ of $x$ in $M$ such that the map $$phi:{(v,w)in N: vin V, |w|<epsilon}toBbb R^n, (v,w)mapsto v+w,$$
is a diffeomorphism between $N_{V,epsilon}$ and its image, where $N$ is the normal bundle of $M$.
Thanks in advance.
differential-geometry
asked Jan 17 at 4:18
DinoDino
1026
$endgroup$
add a comment |
$begingroup$
Let $MsubsetBbb R^n$ be a $C^1$ manifold. I need to prove that for any $xin M$, there exist $epsilon>0$ and a neighborhood $V$ of $x$ in $M$ such that the map $$phi:{(v,w)in N: vin V, |w|<epsilon}toBbb R^n, (v,w)mapsto v+w,$$
is a diffeomorphism between $N_{V,epsilon}$ and its image, where $N$ is the normal bundle of $M$.
Thanks in advance.
differential-geometry
asked Jan 17 at 4:18
DinoDino
1026
$endgroup$
add a comment |
$begingroup$
Let $MsubsetBbb R^n$ be a $C^1$ manifold. I need to prove that for any $xin M$, there exist $epsilon>0$ and a neighborhood $V$ of $x$ in $M$ such that the map $$phi:{(v,w)in N: vin V, |w|<epsilon}toBbb R^n, (v,w)mapsto v+w,$$
is a diffeomorphism between $N_{V,epsilon}$ and its image, where $N$ is the normal bundle of $M$.
Thanks in advance.
differential-geometry
asked Jan 17 at 4:18
DinoDino
1026
$endgroup$
Let $MsubsetBbb R^n$ be a $C^1$ manifold. I need to prove that for any $xin M$, there exist $epsilon>0$ and a neighborhood $V$ of $x$ in $M$ such that the map $$phi:{(v,w)in N: vin V, |w|<epsilon}toBbb R^n, (v,w)mapsto v+w,$$
is a diffeomorphism between $N_{V,epsilon}$ and its image, where $N$ is the normal bundle of $M$.
Thanks in advance.
differential-geometry
differential-geometry
asked Jan 17 at 4:18
DinoDino
1026
asked Jan 17 at 4:18
DinoDino
1026
asked Jan 17 at 4:18
DinoDino
1026
asked Jan 17 at 4:18
DinoDino
1026
asked Jan 17 at 4:18
DinoDino
1026
1026
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
HINT: Compute $Dphi_{(x,0)}colon T_{(x,0)}N to Bbb R^n$. Note that $T_{(x,0)}N cong T_xMoplus N_xM$.
answered Jan 17 at 7:13
Ted ShifrinTed Shifrin
63.9k44591
$endgroup$
add a comment |
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%2f3076586%2flocal-tubular-neighborhood%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
HINT: Compute $Dphi_{(x,0)}colon T_{(x,0)}N to Bbb R^n$. Note that $T_{(x,0)}N cong T_xMoplus N_xM$.
answered Jan 17 at 7:13
Ted ShifrinTed Shifrin
63.9k44591
$endgroup$
add a comment |
$begingroup$
HINT: Compute $Dphi_{(x,0)}colon T_{(x,0)}N to Bbb R^n$. Note that $T_{(x,0)}N cong T_xMoplus N_xM$.
answered Jan 17 at 7:13
Ted ShifrinTed Shifrin
63.9k44591
$endgroup$
add a comment |
$begingroup$
HINT: Compute $Dphi_{(x,0)}colon T_{(x,0)}N to Bbb R^n$. Note that $T_{(x,0)}N cong T_xMoplus N_xM$.
answered Jan 17 at 7:13
Ted ShifrinTed Shifrin
63.9k44591
$endgroup$
HINT: Compute $Dphi_{(x,0)}colon T_{(x,0)}N to Bbb R^n$. Note that $T_{(x,0)}N cong T_xMoplus N_xM$.
answered Jan 17 at 7:13
Ted ShifrinTed Shifrin
63.9k44591
answered Jan 17 at 7:13
Ted ShifrinTed Shifrin
63.9k44591
answered Jan 17 at 7:13
Ted ShifrinTed Shifrin
63.9k44591
answered Jan 17 at 7:13
Ted ShifrinTed Shifrin
63.9k44591
63.9k44591
add a comment |
add a comment |
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%2f3076586%2flocal-tubular-neighborhood%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
