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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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Volume 16, Issue 1

Issues

How many torsionless affine connections exist in general dimension?

Zdenek Dušek
  • University of Ostrava, Department of Mathematics, Faculty of Science, University of Ostrava, 30. dubna 22, 701 03 Ostrava, Czech Republic and Department of Mathematics, Faculty of Science, University of Hradec Králové Rokitanského 62, 500 03 Hradec Králové, Czech Republic
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/ Oldrich Kowalski
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  • Mathematical Institute, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic
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Published Online: 2016-01-16 | DOI: https://doi.org/10.1515/advgeom-2015-0033

Abstract

We study the question how many real analytic torsion-free affine connections exist locally on a smooth manifold M of dimension n. The families of torsion-free connections with skew-symmetric Ricci tensor and those with symmetric Ricci tensor are determined in terms of the number of arbitrary functions of n variables.

Keywords: Affine connection; Ricci tensor; Cauchy-Kowalevski Theorem

About the article

Received: 2014-05-06

Published Online: 2016-01-16

Published in Print: 2016-01-01


Citation Information: Advances in Geometry, Volume 16, Issue 1, Pages 71–76, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2015-0033.

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