Rigidity of Rank-one Factors of Compact Symemtric Spaces
نویسنده
چکیده
Questions of isolation phenomena for minimal submanifolds have been posed for many years. Perhaps the most studied case is for minimal submanifolds of the sphere. Lawson [L1], Chern, do Carmo and Kobayashi [CCK], Barbosa [B], Fischer-Colbrie [FC] and others studied minimal submanifolds of the sphere using a range of techniques and obtained existence and uniqueness results. An important part of this study was initiated by Simons [Si], who used a rigidityisolation result for minimal hypersurfaces of S to show that a minimal cone in euclidean space constructed as a blow-up limit from the given minimal graph was over a totally geodesic subset in the sphere. This was an important part of his extension of the Bernstein theorem to dimensions up to n = 7.
منابع مشابه
Rigidity of Rank-one Factors of Compact Symmetric Spaces
We consider the decomposition of a compact-type symmetric space into a product of factors and show that the rank-one factors, when considered as totally geodesic submanifolds of the space, are isolated from inequivalent minimal submanifolds.
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