publication . Preprint . Article . 2008

Osserman and Conformally Osserman Manifolds with Warped and Twisted Product Structure

Miguel Brozos-Vázquez; Eduardo García-Río; Ramón Vázquez-Lorenzo;
Open Access English
  • Published: 18 Jul 2008
Abstract
We characterize Osserman and conformally Osserman Riemannian manifolds with the local structure of a warped product. By means of this approach we analyze the twisted product structure and obtain, as a consequence, that the only Osserman manifolds which can be written as a twisted product are those of constant curvature. Pseudo-Riemannian versions of those results are also considered, showing that four-dimensional conformally Osserman warped products are locally conformally flat. The result however fails in higher dimensions where there exist conformally Osserman products which are not locally conformally flat.
Subjects
arXiv: Mathematics::Differential GeometryMathematics::Analysis of PDEsQuantitative Biology::Biomolecules
free text keywords: Mathematics - Differential Geometry, 53C20, 53C50, Applied Mathematics, Mathematics (miscellaneous), Manifold, Local structure, Topology, Constant curvature, Mathematical analysis, Mathematics

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