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Definition
Sharp map
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From Wikipedia, the free encyclopedia
Indifferential geometry, the sharp map is the mapping that converts 1-forms into corresponding vectors, given a non-degenerate (0,2)-tensor.
Definition[edit]
Let be a manifold and denote the space of all sections of its tangent bundle. Fix a nondegenerate (0,2)-tensor field , for example a metric tensor or a symplectic form. The definition
-
yields a linear map sometimes called the flat map
-
which is an isomorphism, since is non-degenerate. Its inverse
-
is called the sharp map.
t
e
Retrieved from "https://en.wikipedia.org/w/index.php?title=Sharp_map&oldid=1200580711"
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