Hypersurfaces with Isometric Reeb Flow in Hermitian Symmetric Spaces of Rank 2
نویسنده
چکیده
In this talk, first we introduce the classification of homogeneous hypersurfaces in some Hermitian symmetric spaces of rank 1 or rank 2. In particular, we give a full expression of the geometric structures for hypersurfaces in complex two-plane Grassmannians G2(C) or in complex hyperbolic twoplane Grassmannians G2(C). Next by using the isometric Reeb flow we give a complete classification for hypersurfaces M in complex two-plane Grassmannians G2(C), complex hyperbolic two-plane Grassmannians G2(C) and a complex quadric Qm.
منابع مشابه
Differential Geometry of Real Hypersurfaces in Hermitian Symmetric Spaces with Rank 2 Jürgen Berndt and Young
In this talk, first we introduce the classification of homogeneous hypersurfaces in some Hermitian symmetric spaces of rank 1 or rank 2. In particular, we give a full expression of the geometric structures for hypersurfaces in complex two-plane Grassmannians G2(C) or in complex hyperbolic twoplane Grassmannians G2(C). Next by using the isometric Reeb flow we give a complete classification for h...
متن کاملCoisotropic and polar actions on compact irreducible Hermitian symmetric spaces
We obtain the full classification of coisotropic and polar isometric actions of compact Lie groups on irreducible Hermitian symmetric spaces.
متن کاملA sharp upper bound for the first eigenvalue of the Laplacian of compact hypersurfaces in rank-1 symmetric spaces
M |H| 2, where H is the mean curvature of the hypersurface M. These inequalities of Bleecker–Weiner and Reilly are also sharp for geodesic spheres in Rn. Since then, Reilly’s inequality has been extended to hypersurfaces in other simply connected space forms (see [7] and [8] for details and related results). While trying to understand these results, we noticed that one can obtain a similar shar...
متن کاملQuasi-flats and Rigidity in Higher Rank Symmetric Spaces
In this paper we use elementary geometrical and topological methods to study some questions about the coarse geometry of symmetric spaces. Our results are powerful enough to apply to noncocompact lattices in higher rank symmetric spaces, such as SL(n,Z), n ≥ 3 : Theorem 8.1 is a major step towards the proof of quasiisometric rigidity of such lattices ([E]). We also give a different, and effecti...
متن کاملFord Fundamental Domains in Symmetric Spaces of Rank One
We show the existence of isometric (or Ford) fundamental regions for a large class of subgroups of the isometry group of any rank one Riemannian symmetric space of noncompact type. The proof does not use the classification of symmetric spaces. All hitherto known existence results of isometric fundamental regions and domains are essentially subsumed by our work.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013