“Hadamard manifold”的意思、由来-开放百科全书

词条

Hadamard manifold

释义

Examples
See also
References

In mathematics, a Hadamard manifold, named after Jacques Hadamard — sometimes called a Cartan–Hadamard manifold, after Élie Cartan — is a Riemannian manifold (M, g) that is complete and simply connected and has everywhere non-positive sectional curvature.^[1]^[2]

Examples

The real line R with its usual metric is a Hadamard manifold with constant sectional curvature equal to 0.
Standard n-dimensional hyperbolic space Hⁿ is a Hadamard manifold with constant sectional curvature equal to −1.

References

1. ^{{cite book|last=Li|first=Peter|title=Geometric Analysis|year=2012|publisher=Cambridge University Press|isbn=9781107020641|pages=381}}
2. ^{{cite book|last=Lang|first=Serge|title=Fundamentals of Differential Geometry, Volume 160|year=1989|publisher=Springer|isbn=9780387985930|pages=252–253}}

1 : Riemannian manifolds

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Examples

See also

References