2023/05/12 by Paul-Andi Nagy, Uwe Semmelmann, Nagy, Paul-Andi +1
Mathematics · Physics and Astronomy · #32Q20 #53C15 #53C26 #53C35 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2305.07391
openalex publication_date 2023/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the integrability to second order of infinitesimal Einstein deformations on compact Riemannian and in particular on Kähler manifolds. We find a new way of expressing the necessary and sufficient condition for integrability to second order, which also gives a very clear and compact way of writing the Koiso obstruction. As an application we consider the Kähler case, where the condition can be further simplified and in complex dimension 3 turns out to be purely algebraic. One of our main results is the complete and explicit description of infinitesimal Einstein deformation integrable to second order on the complex 2-plane Grassmannian, which also has a quaternion Kähler structure. As a striking consequence we find that the symmetric Einstein metric on the Grassmannian Gr2(\bbCn+2) for n odd is rigid.