Cylindricity of complete Euclidean submanifolds with relative nullity

We show that a complete Euclidean submanifold with minimal index of relative nullity ν 0 > 0 and Ricci curvature with a certain controlled decay must be a ν 0 -cylinder. This is an extension of the classical Hartman cylindricity theorem.

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Veröffentlicht in:	Annals of global analysis and geometry 2016-04, Vol.49 (3), p.253-257
Hauptverfasser:	Guimarães, Felippe Soares, de Freitas, Guilherme Machado
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Curvature Decomposition Differential Geometry Euclidean geometry Euclidean space Geometry Global Analysis and Analysis on Manifolds Manifolds (mathematics) Mathematical analysis Mathematical models Mathematical Physics Mathematics Mathematics and Statistics Studies Texts Theorems
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Beschreibung
Zusammenfassung:	We show that a complete Euclidean submanifold with minimal index of relative nullity ν 0 > 0 and Ricci curvature with a certain controlled decay must be a ν 0 -cylinder. This is an extension of the classical Hartman cylindricity theorem.
ISSN:	0232-704X 1572-9060
DOI:	10.1007/s10455-015-9490-0