2020
DOI: 10.1007/s10455-020-09742-5
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Complete submanifolds with relative nullity in space forms

Abstract: We use techniques based on the splitting tensor to explicitly integrate the Codazzi equation along the relative nullity distribution and express the second fundamental form in terms of the Jacobi tensor of the ambient space. This approach allows us to easily recover several important results in the literature on complete submanifolds with relative nullity of the sphere as well as derive new strong consequences in hyperbolic and Euclidean spaces. Among the consequences of our main theorem are results on submani… Show more

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Cited by 3 publications
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“…The next result extends Corollary 1 in [3] for hypersurfaces in every space form without any global assumption.…”
Section: Introductionsupporting
confidence: 77%
“…The next result extends Corollary 1 in [3] for hypersurfaces in every space form without any global assumption.…”
Section: Introductionsupporting
confidence: 77%