Conformally flat manifold
A (pseudo-)Riemannian manifold is conformally flat if each point has a neighborhood that can be mapped to flat space by a conformal transformation. More formally, let (M, g) be a pseudo-Riemannian manifold. Then (M, g) is conformally flat if for each point x in M, there exists a neighborhood U of x and a smooth function f defined on U such that (U, e2fg) is flat (i.e. the curvature of e2fg vanishes on U). The function f need not be defined on all of M.
primaryTopic
Conformally flat manifold
A (pseudo-)Riemannian manifold is conformally flat if each point has a neighborhood that can be mapped to flat space by a conformal transformation. More formally, let (M, g) be a pseudo-Riemannian manifold. Then (M, g) is conformally flat if for each point x in M, there exists a neighborhood U of x and a smooth function f defined on U such that (U, e2fg) is flat (i.e. the curvature of e2fg vanishes on U). The function f need not be defined on all of M.
has abstract
A (pseudo-)Riemannian manifold ...... tion f is defined on all of M.
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Конформно плоское многообразие ...... ункция определяется на всём М.
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Wikipage revision ID
708,195,857
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A (pseudo-)Riemannian manifold ...... ed not be defined on all of M.
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Конформно плоское многообразие ...... ункция определяется на всём М.
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label
Conformally flat manifold
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Конформно плоское многообразие
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