Examples of Non-Conformal Submersions from Spheres with Umbilical Fibers
We directly prove that the foliation of the sphere S2n+1, the leaves of which are intersections of all complex linear 2-dimensional subspaces of ℂn+1 translated by a constant vector p, defines a submersion that is horizontally conformal if and only if p=0. We generalise this result to the cases of S...
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De Gruyter
2014-07-01
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| Series: | Demonstratio Mathematica |
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| Online Access: | http://www.degruyter.com/view/j/dema.2014.47.issue-3/dema-2014-0059/dema-2014-0059.xml?format=INT |
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doaj-ab1841daf86541f09ca51feb11e8d3302020-11-24T21:21:04ZengDe GruyterDemonstratio Mathematica0420-12132391-46612014-07-0147373874710.2478/dema-2014-0059dema-2014-0059Examples of Non-Conformal Submersions from Spheres with Umbilical FibersZawadzki Tomasz0FACULTY OF MATHEMATICS AND COMPUTER SCIENCES, UNIVERSITY OF ŁÓDZ Banacha 22 90-238 ŁÓDZ, POLANDWe directly prove that the foliation of the sphere S2n+1, the leaves of which are intersections of all complex linear 2-dimensional subspaces of ℂn+1 translated by a constant vector p, defines a submersion that is horizontally conformal if and only if p=0. We generalise this result to the cases of S4n+3 and S15 with foliations constructed using quaternionic and octonionic structure (resp.) in an analogous wayhttp://www.degruyter.com/view/j/dema.2014.47.issue-3/dema-2014-0059/dema-2014-0059.xml?format=INTand phrases: foliationconformal submersionspheres |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Zawadzki Tomasz |
| spellingShingle |
Zawadzki Tomasz Examples of Non-Conformal Submersions from Spheres with Umbilical Fibers Demonstratio Mathematica and phrases: foliation conformal submersion spheres |
| author_facet |
Zawadzki Tomasz |
| author_sort |
Zawadzki Tomasz |
| title |
Examples of Non-Conformal Submersions from Spheres with Umbilical Fibers |
| title_short |
Examples of Non-Conformal Submersions from Spheres with Umbilical Fibers |
| title_full |
Examples of Non-Conformal Submersions from Spheres with Umbilical Fibers |
| title_fullStr |
Examples of Non-Conformal Submersions from Spheres with Umbilical Fibers |
| title_full_unstemmed |
Examples of Non-Conformal Submersions from Spheres with Umbilical Fibers |
| title_sort |
examples of non-conformal submersions from spheres with umbilical fibers |
| publisher |
De Gruyter |
| series |
Demonstratio Mathematica |
| issn |
0420-1213 2391-4661 |
| publishDate |
2014-07-01 |
| description |
We directly prove that the foliation of the sphere S2n+1, the leaves of which are intersections of all complex linear 2-dimensional subspaces of ℂn+1 translated by a constant vector p, defines a submersion that is horizontally conformal if and only if p=0. We generalise this result to the cases of S4n+3 and S15 with foliations constructed using quaternionic and octonionic structure (resp.) in an analogous way |
| topic |
and phrases: foliation conformal submersion spheres |
| url |
http://www.degruyter.com/view/j/dema.2014.47.issue-3/dema-2014-0059/dema-2014-0059.xml?format=INT |
| work_keys_str_mv |
AT zawadzkitomasz examplesofnonconformalsubmersionsfromsphereswithumbilicalfibers |
| _version_ |
1726001342409867264 |