We find conditions under which a Ricci positive metric can be deformed in a tubular neighbourhood of some submanifold to agree with another given Ricci positive metric. We insist that this final metric has everywhere positive Ricci curvature.
"Deforming Ricci Positive Metrics." Tokyo J. Math. 25 (1) 181 - 189, June 2002. https://doi.org/10.3836/tjm/1244208944