Torsion and the second fundamental form for distributions
The second fundamental form of Riemannian geometry is generalised to the case of a manifold with a linear connection and an integrable distribution. This bilinear form is generally not symmetric and its skew part is the torsion. The form itself is closely related to the shape map of the connection....
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2016-08-01
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| Series: | Communications in Mathematics |
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| Online Access: | https://doi.org/10.1515/cm-2016-0003 |
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doaj-9b98a567f2a84db8b669fa775adcc8032021-09-06T19:19:41ZengSciendoCommunications in Mathematics2336-12982016-08-01241232810.1515/cm-2016-0003cm-2016-0003Torsion and the second fundamental form for distributionsPrince Geoff0Department of Mathematics and Statistics, La Trobe University, Victoria 3086, AustraliaThe second fundamental form of Riemannian geometry is generalised to the case of a manifold with a linear connection and an integrable distribution. This bilinear form is generally not symmetric and its skew part is the torsion. The form itself is closely related to the shape map of the connection. The codimension one case generalises the traditional shape operator of Riemannian geometry.https://doi.org/10.1515/cm-2016-0003torsionsecond fundamental formshape operatorintegrable distributions |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Prince Geoff |
| spellingShingle |
Prince Geoff Torsion and the second fundamental form for distributions Communications in Mathematics torsion second fundamental form shape operator integrable distributions |
| author_facet |
Prince Geoff |
| author_sort |
Prince Geoff |
| title |
Torsion and the second fundamental form for distributions |
| title_short |
Torsion and the second fundamental form for distributions |
| title_full |
Torsion and the second fundamental form for distributions |
| title_fullStr |
Torsion and the second fundamental form for distributions |
| title_full_unstemmed |
Torsion and the second fundamental form for distributions |
| title_sort |
torsion and the second fundamental form for distributions |
| publisher |
Sciendo |
| series |
Communications in Mathematics |
| issn |
2336-1298 |
| publishDate |
2016-08-01 |
| description |
The second fundamental form of Riemannian geometry is generalised to the case of a manifold with a linear connection and an integrable distribution. This bilinear form is generally not symmetric and its skew part is the torsion. The form itself is closely related to the shape map of the connection. The codimension one case generalises the traditional shape operator of Riemannian geometry. |
| topic |
torsion second fundamental form shape operator integrable distributions |
| url |
https://doi.org/10.1515/cm-2016-0003 |
| work_keys_str_mv |
AT princegeoff torsionandthesecondfundamentalformfordistributions |
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1717778075379302400 |