Ricci curvature in the neighborhood of rank-one symmetric spaces

@article{Delay2001RicciCI,
title={Ricci curvature in the neighborhood of rank-one symmetric spaces},
author={Erwann Delay and Marc Herzlich},
journal={The Journal of Geometric Analysis},
year={2001},
volume={11},
pages={573-588}
}
• Published 1 December 2001
• Mathematics
• The Journal of Geometric Analysis
We study the Ricci curvature of a Riemannian metric as a differential operator acting on the space of metrics close (in a weighted functional spaces topology) to the standard metric of a rank-one noncompact symmetric space. We prove that any symmetric bilinear field close enough to the standard may be realized as the Ricci curvature of a unique close metric if its decay rate at infinity (its weight) belongs to some precisely known interval. We also study what happens if the decay rate is too…

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