dc.identifier.uri |
http://dx.doi.org/10.15488/2356 |
|
dc.identifier.uri |
http://www.repo.uni-hannover.de/handle/123456789/2382 |
|
dc.contributor.author |
Rizzi, L.
|
|
dc.contributor.author |
Silveira, P.
|
|
dc.date.accessioned |
2017-11-17T12:10:53Z |
|
dc.date.available |
2019-06-21T22:05:03Z |
|
dc.date.issued |
2017 |
|
dc.identifier.citation |
Rizzi, L.; Silveira, P.: Sub-Riemannian Ricci curvatures and universal diameter bounds for 3-Sasakian manifolds. In: Journal of the Institute of Mathematics of Jussieu 2017 (2017), S. 1-45. DOI: https://doi.org/10.1017/S1474748017000226 |
|
dc.description.abstract |
For a fat sub-Riemannian structure, we introduce three canonical Ricci curvatures in the sense of Agrachev–Zelenko–Li. Under appropriate bounds we prove comparison theorems for conjugate lengths, Bonnet–Myers type results and Laplacian comparison theorems for the intrinsic sub-Laplacian. As an application, we consider the sub-Riemannian structure of 3-Sasakian manifolds, for which we provide explicit curvature formulas. We prove that any complete 3-Sasakian structure of dimension 4d+3, with d>1, has sub-Riemannian diameter bounded by π. When d=1, a similar statement holds under additional Ricci bounds. These results are sharp for the natural sub-Riemannian structure on S4d+3
of the quaternionic Hopf fibrations:
S3↪S4d+3→HPd,
whose exact sub-Riemannian diameter is π, for all d⩾1
. |
eng |
dc.language.iso |
eng |
|
dc.publisher |
Cambridge : Cambridge University Press |
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dc.relation.ispartofseries |
Journal of the Institute of Mathematics of Jussieu 2017 (2017) |
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dc.rights |
Es gilt deutsches Urheberrecht. Das Dokument darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. Dieser Beitrag ist aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich. |
|
dc.subject |
3-Sasakian |
eng |
dc.subject |
53-XX differential geometry |
eng |
dc.subject |
curvature |
eng |
dc.subject |
sub-Riemannian geometry |
eng |
dc.subject.ddc |
510 | Mathematik
|
ger |
dc.title |
Sub-Riemannian Ricci curvatures and universal diameter bounds for 3-Sasakian manifolds |
eng |
dc.type |
Article |
|
dc.type |
Text |
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dc.relation.issn |
1474-7480 |
|
dc.relation.doi |
https://doi.org/10.1017/S1474748017000226 |
|
dc.bibliographicCitation.volume |
2017 |
|
dc.bibliographicCitation.firstPage |
1 |
|
dc.bibliographicCitation.lastPage |
45 |
|
dc.description.version |
publishedVersion |
|
tib.accessRights |
frei zug�nglich |
|