Prescribing Ricci curvature on homogeneous spaces
Prescribing Ricci curvature on homogeneous spaces
Abstract The prescribed Ricci curvature problem in the context of G -invariant metrics on a homogeneous space <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow><m:mi>M</m:mi><m:mo>=</m:mo><m:mrow><m:mi>G</m:mi><m:mo>/</m:mo><m:mi>K</m:mi></m:mrow></m:mrow></m:math> {M=G/K} is studied. We focus on the metrics at which the map <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow><m:mi>g</m:mi><m:mo>↦</m:mo><m:mrow><m:mi>Rc</m:mi><m:mo></m:mo><m:mrow><m:mo stretchy="false">(</m:mo><m:mi>g</m:mi><m:mo stretchy="false">)</m:mo></m:mrow></m:mrow></m:mrow></m:math> {g\mapsto\operatorname{Rc}(g)} is, locally, as injective and surjective as it can be. Our main result is …