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Willie Wong
Willie Wong
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jacktang1996
jacktang1996
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The problem is:

For any closed 2-form in the Minkowski space $\mathbb{R}^{3,1}$ satisfiying $dF=0$ and $\delta F \ne 0$ (with $F$$\delta$ denoting the codifferential), does there exist a Lorentz manifold $(M,g)$ and a corrsponding diffeomorpism $f:M\to\mathbb{R}^{3,1}$ such that the pullback of $F$ on $M$, $f^{*}F$, satisfies $d(f^{*}F)=0$ and $\delta(f^{*}F)=0$?

The problem is:

For any closed 2-form in the Minkowski space $\mathbb{R}^{3,1}$ satisfiying $dF=0$ and $\delta F \ne 0$ (with $F$ denoting the codifferential), does there exist a Lorentz manifold $(M,g)$ and a corrsponding diffeomorpism $f:M\to\mathbb{R}^{3,1}$ such that the pullback of $F$ on $M$, $f^{*}F$, satisfies $d(f^{*}F)=0$ and $\delta(f^{*}F)=0$?

The problem is:

For any closed 2-form in the Minkowski space $\mathbb{R}^{3,1}$ satisfiying $dF=0$ and $\delta F \ne 0$ (with $\delta$ denoting the codifferential), does there exist a Lorentz manifold $(M,g)$ and a corrsponding diffeomorpism $f:M\to\mathbb{R}^{3,1}$ such that the pullback of $F$ on $M$, $f^{*}F$, satisfies $d(f^{*}F)=0$ and $\delta(f^{*}F)=0$?

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jacktang1996
jacktang1996
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A problem about closed 2-forms on Minkowski space

The problem is:

For any closed 2-form in the Minkowski space $\mathbb{R}^{3,1}$ satisfiying $dF=0$ and $\delta F \ne 0$ (with $F$ denoting the codifferential), does there exist a Lorentz manifold $(M,g)$ and a corrsponding diffeomorpism $f:M\to\mathbb{R}^{3,1}$ such that the pullback of $F$ on $M$, $f^{*}F$, satisfies $d(f^{*}F)=0$ and $\delta(f^{*}F)=0$?