Pushforward of a differential Form The 2019 Stack Overflow Developer Survey Results Are InUnderstanding the Schwarz reflection principleConvergence of the sequence of inverses of automorphismsDifferential equation $a_0g+a_1g'+a_2g''+cdots+a_ng^(n)=f$A modified version of Goursat's TheoremWhy Differential Forms on Riemann surfaces?Is $int_-infty ^infty g(z,t),dt$ holomorphic?Is $int_0^infty g(s,u)du$ is holomorphic when $slongmapsto g(s,u)$ is holomorphic?A sequence of holomorphic functions $f_n$ uniformly convergent on boundary of open set.Verification of an example on domain of holomorphyCauchy - Riemann equation conclusion
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Pushforward of a differential Form
The 2019 Stack Overflow Developer Survey Results Are InUnderstanding the Schwarz reflection principleConvergence of the sequence of inverses of automorphismsDifferential equation $a_0g+a_1g'+a_2g''+cdots+a_ng^(n)=f$A modified version of Goursat's TheoremWhy Differential Forms on Riemann surfaces?Is $int_-infty ^infty g(z,t),dt$ holomorphic?Is $int_0^infty g(s,u)du$ is holomorphic when $slongmapsto g(s,u)$ is holomorphic?A sequence of holomorphic functions $f_n$ uniformly convergent on boundary of open set.Verification of an example on domain of holomorphyCauchy - Riemann equation conclusion
$begingroup$
Let $omega = (x-y)dx + (z^2 - x)dy + xydz$ be a 1-holomorphic form in a open subset $U subset mathbbC^3$ and $F : U subset mathbbC^3 longrightarrow mathbbC^3$ defined by : $F(x,y,z) = (x^2, y-z, z^2 + x)$.
What is the pushforward $F_*(omega)$?
Can someone help me? Thank you.
complex-analysis
asked Apr 7 at 20:25
Allain JFAllain JF
11
New contributor
Allain JF is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
Let $omega = (x-y)dx + (z^2 - x)dy + xydz$ be a 1-holomorphic form in a open subset $U subset mathbbC^3$ and $F : U subset mathbbC^3 longrightarrow mathbbC^3$ defined by : $F(x,y,z) = (x^2, y-z, z^2 + x)$.
What is the pushforward $F_*(omega)$?
Can someone help me? Thank you.
complex-analysis
asked Apr 7 at 20:25
Allain JFAllain JF
11
New contributor
Allain JF is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
1
$begingroup$
Welcome to Math.SE. Please include in your post the attempt you made to solve your question.
$endgroup$
– Ertxiem
Apr 7 at 20:33
$begingroup$
In general the pushforward of a differential form is not well-defined, but for a diffeomorphism $F$ one defines $F_*omega:=(F^-1)^*omega$.
$endgroup$
– Andrea
Apr 7 at 20:33
$begingroup$
Ok, Andrea. Thank you !!
$endgroup$
– Allain JF
Apr 7 at 20:44
add a comment |
$begingroup$
Let $omega = (x-y)dx + (z^2 - x)dy + xydz$ be a 1-holomorphic form in a open subset $U subset mathbbC^3$ and $F : U subset mathbbC^3 longrightarrow mathbbC^3$ defined by : $F(x,y,z) = (x^2, y-z, z^2 + x)$.
What is the pushforward $F_*(omega)$?
Can someone help me? Thank you.
complex-analysis
asked Apr 7 at 20:25
Allain JFAllain JF
11
New contributor
Allain JF is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Let $omega = (x-y)dx + (z^2 - x)dy + xydz$ be a 1-holomorphic form in a open subset $U subset mathbbC^3$ and $F : U subset mathbbC^3 longrightarrow mathbbC^3$ defined by : $F(x,y,z) = (x^2, y-z, z^2 + x)$.
What is the pushforward $F_*(omega)$?
Can someone help me? Thank you.
complex-analysis
complex-analysis
asked Apr 7 at 20:25
Allain JFAllain JF
11
New contributor
Allain JF is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Apr 7 at 20:25
Allain JFAllain JF
11
New contributor
Allain JF is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Apr 7 at 20:31
Allain JF
asked Apr 7 at 20:25
Allain JFAllain JF
11
New contributor
Allain JF is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Apr 7 at 20:25
Allain JFAllain JF
11
asked Apr 7 at 20:25
Allain JFAllain JF
11
11
New contributor
Allain JF is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Allain JF is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Allain JF is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
$begingroup$
Welcome to Math.SE. Please include in your post the attempt you made to solve your question.
$endgroup$
– Ertxiem
Apr 7 at 20:33
$begingroup$
In general the pushforward of a differential form is not well-defined, but for a diffeomorphism $F$ one defines $F_*omega:=(F^-1)^*omega$.
$endgroup$
– Andrea
Apr 7 at 20:33
$begingroup$
Ok, Andrea. Thank you !!
$endgroup$
– Allain JF
Apr 7 at 20:44
add a comment |
1
$begingroup$
Welcome to Math.SE. Please include in your post the attempt you made to solve your question.
$endgroup$
– Ertxiem
Apr 7 at 20:33
$begingroup$
In general the pushforward of a differential form is not well-defined, but for a diffeomorphism $F$ one defines $F_*omega:=(F^-1)^*omega$.
$endgroup$
– Andrea
Apr 7 at 20:33
$begingroup$
Ok, Andrea. Thank you !!
$endgroup$
– Allain JF
Apr 7 at 20:44
1
1
$begingroup$
Welcome to Math.SE. Please include in your post the attempt you made to solve your question.
$endgroup$
– Ertxiem
Apr 7 at 20:33
$begingroup$
Welcome to Math.SE. Please include in your post the attempt you made to solve your question.
$endgroup$
– Ertxiem
Apr 7 at 20:33
$begingroup$
In general the pushforward of a differential form is not well-defined, but for a diffeomorphism $F$ one defines $F_*omega:=(F^-1)^*omega$.
$endgroup$
– Andrea
Apr 7 at 20:33
$begingroup$
In general the pushforward of a differential form is not well-defined, but for a diffeomorphism $F$ one defines $F_*omega:=(F^-1)^*omega$.
$endgroup$
– Andrea
Apr 7 at 20:33
$begingroup$
Ok, Andrea. Thank you !!
$endgroup$
– Allain JF
Apr 7 at 20:44
$begingroup$
Ok, Andrea. Thank you !!
$endgroup$
– Allain JF
Apr 7 at 20:44
add a comment |
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$begingroup$
Welcome to Math.SE. Please include in your post the attempt you made to solve your question.
$endgroup$
– Ertxiem
Apr 7 at 20:33
$begingroup$
In general the pushforward of a differential form is not well-defined, but for a diffeomorphism $F$ one defines $F_*omega:=(F^-1)^*omega$.
$endgroup$
– Andrea
Apr 7 at 20:33
$begingroup$
Ok, Andrea. Thank you !!
$endgroup$
– Allain JF
Apr 7 at 20:44