Higher order valued reduction theorems for classical connections

Josef Janyška

Open Mathematics (2005)

  • Volume: 3, Issue: 2, page 294-308
  • ISSN: 2391-5455

Abstract

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We generalize reduction theorems for classical connections to operators with values in k-th order natural bundles. Using the 2nd order valued reduction theorems we classify all (0,2)-tensor fields on the cotangent bundle of a manifold with a linear (non-symmetric) connection.

How to cite

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Josef Janyška. "Higher order valued reduction theorems for classical connections." Open Mathematics 3.2 (2005): 294-308. <http://eudml.org/doc/268789>.

@article{JosefJanyška2005,
abstract = {We generalize reduction theorems for classical connections to operators with values in k-th order natural bundles. Using the 2nd order valued reduction theorems we classify all (0,2)-tensor fields on the cotangent bundle of a manifold with a linear (non-symmetric) connection.},
author = {Josef Janyška},
journal = {Open Mathematics},
keywords = {53C05; 58A32; 58A20},
language = {eng},
number = {2},
pages = {294-308},
title = {Higher order valued reduction theorems for classical connections},
url = {http://eudml.org/doc/268789},
volume = {3},
year = {2005},
}

TY - JOUR
AU - Josef Janyška
TI - Higher order valued reduction theorems for classical connections
JO - Open Mathematics
PY - 2005
VL - 3
IS - 2
SP - 294
EP - 308
AB - We generalize reduction theorems for classical connections to operators with values in k-th order natural bundles. Using the 2nd order valued reduction theorems we classify all (0,2)-tensor fields on the cotangent bundle of a manifold with a linear (non-symmetric) connection.
LA - eng
KW - 53C05; 58A32; 58A20
UR - http://eudml.org/doc/268789
ER -

References

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  3. [3] J. Janyška: “Natural vector fields and 2-vector fields on the tangent bundle of a pseudo-Riemannian manifold”, Arch. Math. (Brno), Vol. 37, (2001), pp. 143–160. Zbl1090.58007
  4. [4] J. Janyška: “On the curvature of tensor product connections and covariant differentials”, In: Proc. of the 23rd Winter School Geometry and Physics, Srní (Czech Republic) 2003; Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II, Vol. 72, (2004), pp. 135–143. Zbl1051.53017
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