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Laithy
Laithy
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Let $(M,g)$ be a $n$-dimensional Riemannian manifold with smooth metric $g$.

Proposition 3.2 in the paper "The Boost Problem in General Relativity" by O'Murchadha and Chistodoulou claims that any conformal Killing field will satisfy the third order PDE: $$\nabla^3 X = A\cdot \nabla X + B \cdot X$$ where $A$ and $B$ are linear combination of $Ric$$\text{Riem}$ and $\nabla Ric$$\nabla\text{Riem}$ respectively. Does anyone know a proof of this? Any reference is appreciated.

Let $(M,g)$ be a $n$-dimensional Riemannian manifold with smooth metric $g$.

Proposition 3.2 in the paper "The Boost Problem in General Relativity" by O'Murchadha and Chistodoulou claims that any conformal Killing field will satisfy the third order PDE: $$\nabla^3 X = A\cdot \nabla X + B \cdot X$$ where $A$ and $B$ are linear combination of $Ric$ and $\nabla Ric$ respectively. Does anyone know a proof of this? Any reference is appreciated.

Let $(M,g)$ be a $n$-dimensional Riemannian manifold with smooth metric $g$.

Proposition 3.2 in the paper "The Boost Problem in General Relativity" by O'Murchadha and Chistodoulou claims that any conformal Killing field will satisfy the third order PDE: $$\nabla^3 X = A\cdot \nabla X + B \cdot X$$ where $A$ and $B$ are linear combination of $\text{Riem}$ and $\nabla\text{Riem}$ respectively. Does anyone know a proof of this? Any reference is appreciated.

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Igor Khavkine
Igor Khavkine
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Let $(M,g)$ be a $n$-dimensional Riemannian manifold with smooth metric $g$.

Proposition 3.2 in the paper "The Boost Problem in General Relativity""The Boost Problem in General Relativity" by MurchadhaO'Murchadha and ChistoudouloChistodoulou claims that any conformal Killing field will satisfy the third order PDE: $$\nabla^3 X = A\cdot \nabla X + B \cdot X$$ where $A$ and $B$ are linear combination of $Ric$ and $\nabla Ric$ respectively. Does anyone know a proof of this? Any reference is appreciated.

Let $(M,g)$ be a $n$-dimensional Riemannian manifold with smooth metric $g$.

Proposition 3.2 in the paper "The Boost Problem in General Relativity" by Murchadha and Chistoudoulo claims that any conformal Killing field will satisfy the third order PDE: $$\nabla^3 X = A\cdot \nabla X + B \cdot X$$ where $A$ and $B$ are linear combination of $Ric$ and $\nabla Ric$ respectively. Does anyone know a proof of this? Any reference is appreciated.

Let $(M,g)$ be a $n$-dimensional Riemannian manifold with smooth metric $g$.

Proposition 3.2 in the paper "The Boost Problem in General Relativity" by O'Murchadha and Chistodoulou claims that any conformal Killing field will satisfy the third order PDE: $$\nabla^3 X = A\cdot \nabla X + B \cdot X$$ where $A$ and $B$ are linear combination of $Ric$ and $\nabla Ric$ respectively. Does anyone know a proof of this? Any reference is appreciated.

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Laithy
Laithy
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Conformal Killing fields satisfy a third order PDE

Let $(M,g)$ be a $n$-dimensional Riemannian manifold with smooth metric $g$.

Proposition 3.2 in the paper "The Boost Problem in General Relativity" by Murchadha and Chistoudoulo claims that any conformal Killing field will satisfy the third order PDE: $$\nabla^3 X = A\cdot \nabla X + B \cdot X$$ where $A$ and $B$ are linear combination of $Ric$ and $\nabla Ric$ respectively. Does anyone know a proof of this? Any reference is appreciated.