Rank rigidity for foliations by manifolds of nonpositive curvature

S. Adams

doi:10.1016/0926-2245(93)90022-S

Rank rigidity for foliations by manifolds of nonpositive curvature

S. Adams

Research output: Contribution to journal › Article › peer-review

Abstract

We develop a rank rigidity theorem for finite volume foliations by manifolds of nonpositive sectional curvature. It implies that if the leaves are irreducible Hadamard manifolds of geometric rank ≥ 2, then the leaves are symmetric.

Original language	English (US)
Pages (from-to)	47-70
Number of pages	24
Journal	Differential Geometry and its Applications
Volume	3
Issue number	1
DOIs	https://doi.org/10.1016/0926-2245(93)90022-S
State	Published - Mar 1993
Externally published	Yes

Bibliographical note

Funding Information:
by NSF Postdoctoral

Keywords

Rank rigidity
foliations
nonpositive curvature

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10.1016/0926-2245(93)90022-S

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title = "Rank rigidity for foliations by manifolds of nonpositive curvature",

abstract = "We develop a rank rigidity theorem for finite volume foliations by manifolds of nonpositive sectional curvature. It implies that if the leaves are irreducible Hadamard manifolds of geometric rank ≥ 2, then the leaves are symmetric.",

keywords = "Rank rigidity, foliations, nonpositive curvature",

author = "S. Adams",

note = "Funding Information: by NSF Postdoctoral",

year = "1993",

month = mar,

doi = "10.1016/0926-2245(93)90022-S",

language = "English (US)",

volume = "3",

pages = "47--70",

journal = "Differential Geometry and its Applications",

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N1 - Funding Information: by NSF Postdoctoral

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N2 - We develop a rank rigidity theorem for finite volume foliations by manifolds of nonpositive sectional curvature. It implies that if the leaves are irreducible Hadamard manifolds of geometric rank ≥ 2, then the leaves are symmetric.

AB - We develop a rank rigidity theorem for finite volume foliations by manifolds of nonpositive sectional curvature. It implies that if the leaves are irreducible Hadamard manifolds of geometric rank ≥ 2, then the leaves are symmetric.

KW - Rank rigidity

KW - foliations

KW - nonpositive curvature

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