Kähler–Einstein submanifolds of the infinite dimensional projective space
نویسندگان
چکیده
منابع مشابه
Kähler–Einstein submanifolds of the infinite dimensional projective space
This paper consists of two main results. In the first one we describe all Kähler immersions of a bounded symmetric domain into the infinite dimensional complex projective space in terms of the Wallach set of the domain. In the second one we exhibit an example of complete and nonhomogeneous Kähler-Einstein metric with negative scalar curvature which admits a Kähler immersion into the infinite di...
متن کاملDifferential Geometry of Submanifolds of Projective Space
These are lecture notes on the rigidity of submanifolds of projective space “resembling” compact Hermitian symmetric spaces in their homogeneous embeddings. The results of [16, 20, 29, 18, 19, 10, 31] are surveyed, along with their classical predecessors. The notes include an introduction to moving frames in projective geometry, an exposition of the Hwang-Yamaguchi ridgidity theorem and a new v...
متن کاملWillmore Lagrangian Submanifolds in Complex Projective Space
Let M be an n -dimensional compact Willmore Lagrangian submanifold in a complex projective space CPn and let S and H be the squared norm of the second fundamental form and the mean curvature of M . Denote by ρ2 = S−nH2 the non-negative function on M , K and Q the functions which assign to each point of M the infimum of the sectional curvature and Ricci curvature at the point. We prove some inte...
متن کاملHomogeneity of infinite dimensional isoparametric submanifolds
A subset S of a Riemannian manifoldN is called extrinsically homogeneous if S is an orbit of a subgroup of the isometry group of N . In [Th], Thorbergsson proved the remarkable result that every complete, connected, full, irreducible isoparametric submanifold of a finite dimensional Euclidean space of rank at least 3 is extrinsically homogeneous. This result, combined with results of [PT1] and ...
متن کاملDifferential Geometry of Submanifolds of Projective Space: Rough Draft
• Introduction to the local differential geometry of submanifolds of projective space • Introduction to moving frames for projective geometry • How much must a submanifold X ⊂ PN resemble a given submanifold Z ⊂ PM infinitesimally before we can conclude X ≃ Z? • To what order must a line field on a submanifold X ⊂ PN have contact with X before we can conclude the lines are contained in X? • App...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2010
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s00208-010-0554-y