2021/12/29 by Yuri Nikolayevsky, Nikolayevsky, Yuri, JeongHyeong Park +1
Mathematics · Physics and Astronomy · #53B25 #53C25 #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.2112.14394
openalex publication_date 2021/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that if M is an Einstein hypersurface in an irreducible Riemannian symmetric space M of rank greater than 1 (the classification in the rank-one case was previously known), then either M is of noncompact type and M is a codimension one Einstein solvmanifold, or M=SU(3)/SO(3) (respectively, M=SL(3)/SO(3)) and M is foliated by totally geodesic spheres (respectively, hyperbolic planes) of M, with the space of leaves parametrised by a special Legendrian surface in S5 (respectively, by a proper affine sphere in ℝ3).