About: Almost-contact manifold

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In the mathematical field of differential geometry, an almost-contact structure is a certain kind of geometric structure on a smooth manifold. Such structures were introduced by Shigeo Sasaki in 1960. Precisely, given a smooth manifold an almost-contact structure consists of a hyperplane distribution an almost-complex structure on and a vector field which is transverse to That is, for each point of one selects a codimension-one linear subspace of the tangent space a linear map such that and an element of which is not contained in * for any *

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rdfs:label	Almost-contact manifold (en)
rdfs:comment	In the mathematical field of differential geometry, an almost-contact structure is a certain kind of geometric structure on a smooth manifold. Such structures were introduced by Shigeo Sasaki in 1960. Precisely, given a smooth manifold an almost-contact structure consists of a hyperplane distribution an almost-complex structure on and a vector field which is transverse to That is, for each point of one selects a codimension-one linear subspace of the tangent space a linear map such that and an element of which is not contained in * for any * (en)
dct:subject	Smooth manifolds Differential geometry
Wikipage page ID	65636660 (xsd:integer)
Wikipage revision ID	1104039609 (xsd:integer)
Link from a Wikipage to another Wikipage	Smooth manifolds Vector field Differential geometry Tangent space Distribution (differential geometry) Linear map Linear subspace Direct sum Tensor field Kernel (linear algebra) Differential geometry Linear form Shigeo Sasaki Smooth manifold Almost-complex structure
sameAs	Almost-contact manifold Almost-contact manifold
dbp:wikiPageUsesTemplate	dbt:Cite_journal dbt:Closed_access dbt:Doi dbt:ISBN dbt:No_footnotes dbt:Reflist dbt:Manifolds
has abstract	In the mathematical field of differential geometry, an almost-contact structure is a certain kind of geometric structure on a smooth manifold. Such structures were introduced by Shigeo Sasaki in 1960. Precisely, given a smooth manifold an almost-contact structure consists of a hyperplane distribution an almost-complex structure on and a vector field which is transverse to That is, for each point of one selects a codimension-one linear subspace of the tangent space a linear map such that and an element of which is not contained in Given such data, one can define, for each in a linear map and a linear map by This defines a one-form and (1,1)-tensor field on and one can check directly, by decomposing relative to the direct sum decomposition thatfor any in Conversely, one may define an almost-contact structure as a triple which satisfies the two conditions * for any * Then one can define to be the kernel of the linear map and one can check that the restriction of to is valued in thereby defining (en)
prov:wasDerivedFrom	wikipedia-en:Almost-contact_manifold?oldid=1104039609&ns=0
page length (characters) of wiki page	2970 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Almost-contact_manifold
is Link from a Wikipage to another Wikipage of	Kenmotsu manifold Neda Bokan
is foaf:primaryTopic of	wikipedia-en:Almost-contact_manifold

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