Two remarks on $PQ^{\epsilon}$-projectivity of Riemannian metrics

Vladimir S. Matveev; Stefan Rosemann

doi:10.1017/S0017089512000390

Two remarks on $PQ^{\epsilon}$-projectivity of Riemannian metrics

Differential Geometry 2013-01-14 v1

Authors: Vladimir S. Matveev , Stefan Rosemann

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Abstract

We show that $PQ^{\epsilon}$ -projectivity of two Riemannian metrics introduced in \cite{Top2003} implies affine equivalence of the metrics unless $\epsilon\in\{0,-1,-3,-5,-7,...\}$ . Moreover, we show that for $\epsilon=0$ , $PQ^{\epsilon}$ -projectivity implies projective equivalence.

Keywords

PQ^epsilon-projectivity Riemannian metrics affine equivalence projective equivalence differential geometry

Cite

@article{arxiv.1108.2965,
  title  = {Two remarks on $PQ^{\epsilon}$-projectivity of Riemannian metrics},
  author = {Vladimir S. Matveev and Stefan Rosemann},
  journal= {arXiv preprint arXiv:1108.2965},
  year   = {2013}
}

Comments

6 pages, 2 figures

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