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Communications in Mathematics

Editor-in-Chief: Rossi, Olga

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Mathematical Citation Quotient (MCQ) 2016: 0.28

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Torsion and the second fundamental form for distributions

Geoff Prince
  • Department of Mathematics and Statistics, La Trobe University, Victoria 3086, Australia
  • The Australian Mathematical Sciences Institute, c/o The University of Melbourne, Victoria 3010, Australia
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Published Online: 2016-08-20 | DOI: https://doi.org/10.1515/cm-2016-0003


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.

Keywords: Torsion; second fundamental form; shape operator; integrable distributions


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About the article

Received: 2016-04-21

Accepted: 2016-05-19

Published Online: 2016-08-20

Published in Print: 2016-08-01

Citation Information: Communications in Mathematics, Volume 24, Issue 1, Pages 23–28, ISSN (Online) 2336-1298, DOI: https://doi.org/10.1515/cm-2016-0003.

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© 2016. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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