A canonical connection associated with certain G -structures.



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Sierra, José M. and Valdés Morales, Antonio (1997) A canonical connection associated with certain G -structures. Czechoslovak Mathematical Journal, 47 (1). pp. 73-82. ISSN 0011-4642

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Official URL: http://link.springer.com/content/pdf/10.1023%2FA%3A1022440104951.pdf


Let P be a G-structure on a manifold M and AdP be the adjoint bundle of P. The authors deduce the following main result: there exists a unique connection r adapted to P such that trace(S iX Tor(r)) = 0 for every section S of AdP and every vector field X on M, provided Tor(r) stands for the torsion tensor field of r. Two examples, namely almost Hermitian structures and almost contact metric structures, are discussed in more detail. Another interesting result reads: for a given structure group G, if it is possible to attach a connection to each G-structure in a functorial way with the additional assumption that the connection depends on first order contact only, then the first prolongation of the Lie algebra of G vanishes

Item Type:Article
Uncontrolled Keywords:G-structure; connection; natural connection; torsion
Subjects:Sciences > Mathematics > Differential geometry
ID Code:22454
Deposited On:19 Jul 2013 07:51
Last Modified:12 Dec 2018 15:13

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