Combinatorial differential geometry and ideal Bianchi–Ricci identities II - the torsion case
| Authors | |
|---|---|
| Year of publication | 2012 |
| Type | Article in Periodical |
| Magazine / Source | Archivum Mathematicum |
| MU Faculty or unit | |
| Citation | |
| Web | http://emis.muni.cz/journals/AM/12-1/am2052.pdf |
| Doi | http://dx.doi.org/10.5817/AM2012-1-61 |
| Field | General mathematics |
| Keywords | Natural operator; linear connection; torsion; reduction theorem; graph |
| Attached files | |
| Description | This paper is a continuation of the paper J. Janyška and M. Markl, Combinatorial differential geometry and ideal Bianchi-Ricci identities, Advances in Geometry 11 (2011) 509-540, dealing with a general, not-necessarily torsion-free, connection. It characterizes all possible systems of generators for vector-field valued operators that depend naturally on a set of vector fields and a linear connection, describes the size of the space of such operators and proves the existence of an `ideal' basis consisting of operators with given leading terms which satisfy the (generalized) Bianchi--Ricci identities without corrections. |
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