Double tangent bundle (original) (raw)
In mathematics, particularly differential topology, the double tangent bundle or the second tangent bundle refers to the tangent bundle (TTM,πTTM,TM) of the total space TM of the tangent bundle (TM,πTM,M) of a smooth manifold M. A note on notation: in this article, we denote projection maps by their domains, e.g., πTTM : TTM → TM. Some authors index these maps by their ranges instead, so for them, that map would be written πTM.
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| dbo:abstract | In mathematics, particularly differential topology, the double tangent bundle or the second tangent bundle refers to the tangent bundle (TTM,πTTM,TM) of the total space TM of the tangent bundle (TM,πTM,M) of a smooth manifold M. A note on notation: in this article, we denote projection maps by their domains, e.g., πTTM : TTM → TM. Some authors index these maps by their ranges instead, so for them, that map would be written πTM. The second tangent bundle arises in the study of connections and second order ordinary differential equations, i.e., (semi)spray structures on smooth manifolds, and it is not to be confused with the second order jet bundle. (en) |
| dbo:wikiPageID | 19254708 (xsd:integer) |
| dbo:wikiPageLength | 10019 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID | 982503559 (xsd:integer) |
| dbo:wikiPageWikiLink | dbr:Double_vector_bundle dbc:Differential_geometry dbr:Mathematics dbr:Tangent_bundle dbr:Ehresmann_connection dbr:Connection_(vector_bundle) dbr:Spray_(mathematics) dbc:Topology dbr:Finsler_manifold dbr:Parametrization_(geometry) dbr:Differential_topology dbr:Jet_bundle dbr:Differentiable_manifold dbr:Secondary_vector_bundle_structure dbr:Vector_bundle |
| dbp:date | September 2015 (en) |
| dbp:reason | What makes a reparametrization positive? (en) |
| dbp:wikiPageUsesTemplate | dbt:Jargon-inline |
| dct:subject | dbc:Differential_geometry dbc:Topology |
| rdfs:comment | In mathematics, particularly differential topology, the double tangent bundle or the second tangent bundle refers to the tangent bundle (TTM,πTTM,TM) of the total space TM of the tangent bundle (TM,πTM,M) of a smooth manifold M. A note on notation: in this article, we denote projection maps by their domains, e.g., πTTM : TTM → TM. Some authors index these maps by their ranges instead, so for them, that map would be written πTM. (en) |
| rdfs:label | Double tangent bundle (en) |
| owl:sameAs | freebase:Double tangent bundle wikidata:Double tangent bundle https://global.dbpedia.org/id/4irnu |
| prov:wasDerivedFrom | wikipedia-en:Double_tangent_bundle?oldid=982503559&ns=0 |
| foaf:isPrimaryTopicOf | wikipedia-en:Double_tangent_bundle |
| is dbo:wikiPageWikiLink of | dbr:Double_vector_bundle dbr:Tangent_bundle dbr:Geodesic dbr:Spray_(mathematics) dbr:Exponential_map_(Riemannian_geometry) dbr:Finsler_manifold dbr:Secondary_vector_bundle_structure |
| is foaf:primaryTopic of | wikipedia-en:Double_tangent_bundle |