Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/112197
DC Field | Value | Language |
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dc.contributor.author | Camarinha, Margarida | - |
dc.contributor.author | Raffaelli, Matteo | - |
dc.date.accessioned | 2024-01-24T10:59:42Z | - |
dc.date.available | 2024-01-24T10:59:42Z | - |
dc.date.issued | 2020-03-27 | - |
dc.identifier.issn | 0129-167X | pt |
dc.identifier.issn | 1793-6519 | pt |
dc.identifier.uri | https://hdl.handle.net/10316/112197 | - |
dc.description | 12 pages, no figures. Some changes in section 1; Theorem 1.5 and Corollary 1.7 corrected. To appear in International Journal of Mathematics | pt |
dc.description.abstract | We study semi-Riemannian submanifolds of arbitrary codimension in a Lie group $G$ equipped with a bi-invariant metric. In particular, we show that, if the normal bundle of $M \subset G$ is closed under the Lie bracket, then any normal Jacobi operator $K$ of $M$ equals the square of the associated invariant shape operator $\alpha$. This permits to understand curvature adaptedness to $G$ geometrically, in terms of left translations. For example, in the case where $M$ is a Riemannian hypersurface, our main result states that the normal Jacobi operator commutes with the ordinary shape operator precisely when the left-invariant extension of each of its eigenspaces has first-order tangency with $M$ along all the others. As a further consequence of the equality $K = \alpha^{2}$, we obtain a new case-independent proof of a well-known fact: every three-dimensional Lie group equipped with a bi-invariant semi-Riemannian metric has constant curvature. | pt |
dc.language.iso | eng | pt |
dc.publisher | World Scientific | pt |
dc.rights | openAccess | pt |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | pt |
dc.subject | Mathematics - Differential Geometry | pt |
dc.subject | Mathematics - Differential Geometry | pt |
dc.subject | 53C40 (Primary) 53B25, 53C30 (Secondary) | pt |
dc.title | Curvature-adapted submanifolds of semi-Riemannian groups | pt |
dc.type | article | - |
degois.publication.firstPage | 2350053 | pt |
degois.publication.issue | 09 | pt |
degois.publication.title | International Journal of Mathematics | pt |
dc.peerreviewed | yes | pt |
dc.identifier.doi | 10.1142/S0129167X23500532 | pt |
degois.publication.volume | 34 | pt |
dc.date.embargo | 2020-03-27 | * |
uc.date.periodoEmbargo | 0 | pt |
item.languageiso639-1 | en | - |
item.grantfulltext | open | - |
item.fulltext | Com Texto completo | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
item.openairetype | article | - |
item.cerifentitytype | Publications | - |
Appears in Collections: | FCTUC Matemática - Artigos em Revistas Internacionais I&D CMUC - Artigos em Revistas Internacionais |
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File | Description | Size | Format | |
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Curvature-adapted submanifolds of semi-Riemannian groups.pdf | 379.7 kB | Adobe PDF | View/Open |
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