Stability of Einstein metrics on symmetric spaces of compact type
Stability of Einstein metrics on symmetric spaces of compact type
Abstract We prove the linear stability with respect to the Einstein-Hilbert action of the symmetric spaces $${\text {SU}}(n)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mtext>SU</mml:mtext><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> , $$n\ge 3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>n</mml:mi><mml:mo>≥</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math> , and $$E_6/F_4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn>6</mml:mn></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math> . Combined with earlier results, this resolves the stability problem for irreducible symmetric spaces of compact type.