Displaying similar documents to “A Tensorial Curvature and a Theorem of Chern.”

Natural operators in the view of Cartan geometries

Martin Panák (2003)

Archivum Mathematicum

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We prove, that r -th order gauge natural operators on the bundle of Cartan connections with a target in the gauge natural bundles of the order ( 1 , 0 ) (“tensor bundles”) factorize through the curvature and its invariant derivatives up to order r - 1 . On the course to this result we also prove that the invariant derivations (a generalization of the covariant derivation for Cartan geometries) of the curvature function of a Cartan connection have the tensor character. A modification of the theorem...

Unit tangent sphere bundles with constant scalar curvature

Eric Boeckx, Lieven Vanhecke (2001)

Czechoslovak Mathematical Journal

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As a first step in the search for curvature homogeneous unit tangent sphere bundles we derive necessary and sufficient conditions for a manifold to have a unit tangent sphere bundle with constant scalar curvature. We give complete classifications for low dimensions and for conformally flat manifolds. Further, we determine when the unit tangent sphere bundle is Einstein or Ricci-parallel.