2025-02-22T11:29:16-05:00 DEBUG: VuFindSearch\Backend\Solr\Connector: Query fl=%2A&wt=json&json.nl=arrarr&q=id%3A%22irk-123456789-6308%22&qt=morelikethis&rows=5
2025-02-22T11:29:16-05:00 DEBUG: VuFindSearch\Backend\Solr\Connector: => GET http://localhost:8983/solr/biblio/select?fl=%2A&wt=json&json.nl=arrarr&q=id%3A%22irk-123456789-6308%22&qt=morelikethis&rows=5
2025-02-22T11:29:16-05:00 DEBUG: VuFindSearch\Backend\Solr\Connector: <= 200 OK
2025-02-22T11:29:16-05:00 DEBUG: Deserialized SOLR response
Hyperplanar Webs and Euler Equations

Hyperplanar Webs and Euler Equations

We find necessary and sufficient conditions for the foliation defined by level sets of a function f(x1, . . . , xn) to be totally geodesic in a torsion-free connection and apply them to find the conditions for d-webs of hypersurfaces to be geodesic, and in the case of flat connections, for d-webs (d...

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Bibliographic Details
Main Authors: Goldberg, V.V., Lychagin, V.V.
Format: Article
Language:English
Published: Інститут математики НАН України 2009
Subjects:
Геометрія, топологія та їх застосування
Праці міжнародної конференції "Геометрія в Одесі - 2008"
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/6308
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Summary:We find necessary and sufficient conditions for the foliation defined by level sets of a function f(x1, . . . , xn) to be totally geodesic in a torsion-free connection and apply them to find the conditions for d-webs of hypersurfaces to be geodesic, and in the case of flat connections, for d-webs (d ≥ n + 1) of hypersurfaces to be hyperplanar webs. These conditions are systems of generalized Euler equations, and for flat connections we give an explicit construction of their solutions.

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