The reflection principle for minimal submanifolds of Riemannian symmetric spaces
نویسندگان
چکیده
منابع مشابه
Symmetric Submanifolds of Riemannian Symmetric Spaces
A symmetric space is a Riemannian manifold that is “symmetric” about each of its points: for each p ∈M there is an isometry σp of M such that (σp)∗ = −I on TpM . Symmetric spaces and their local versions were studied and classified by E.Cartan in the 1920’s. In 1980 D.Ferus [F2] introduced the concept of symmetric submanifolds of Euclidean space: A submanifold M of R is a symmetric submanifold ...
متن کاملTotally geodesic submanifolds in Riemannian symmetric spaces
In the first part of this expository article, the most important constructions and classification results concerning totally geodesic submanifolds in Riemannian symmetric spaces are summarized. In the second part, I describe the results of my classification of the totally geodesic submanifolds in the Riemannian symmetric spaces of rank 2. To appear in the Proceedings volume for the conference V...
متن کاملTotally geodesic submanifolds of the exceptional Riemannian symmetric spaces of rank 2
The present article is the final part of a series on the classification of the totally geodesic submanifolds of the irreducible Riemannian symmetric spaces of rank 2. After this problem has been solved for the 2-Grassmannians in my papers [K1] and [K2], and for the space SU(3)/SO(3) in Section 6 of [K3], we now solve the classification for the remaining irreducible Riemannian symmetric spaces o...
متن کاملRelative Isoperimetric Inequality for Minimal Submanifolds in a Riemannian Manifold
Let Σ be a domain on an m-dimensional minimal submanifold in the outside of a convex set C in S or H. The modified volume M Σ is introduced by Choe and Gulliver 1992 and we prove a sharp modified relative isoperimetric inequality for the domain Σ, 1/2 mωmM Σ m−1 ≤ Volume ∂Σ−∂C , where ωm is the volume of the unit ball of R. For any domain Σ on a minimal surface in the outside convex set C in an...
متن کاملBeurling’s Theorem for Riemannian Symmetric Spaces Ii
We prove two versions of Beurling’s theorem for Riemannian symmetric spaces of arbitrary rank. One of them uses the group Fourier transform and the other uses the Helgason Fourier transform. This is the master theorem in the quantitative uncertainty principle.
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: Journal of Differential Geometry
سال: 1973
ISSN: 0022-040X
DOI: 10.4310/jdg/1214431489