Totally Geodesic Surfaces of Riemannian Symmetric Spaces

2014 ◽  
pp. 301-308 ◽  
Author(s):  
Katsuya Mashimo
Keyword(s):  
Symmetric Spaces ◽  
Totally Geodesic ◽  
Riemannian Symmetric Spaces ◽  
Geodesic Surfaces

scholarly journals On the index of symmetric spaces

2018 ◽  
Vol 2018 (737) ◽  
pp. 33-48 ◽  
Author(s):  
Jürgen Berndt ◽  
Carlos Olmos
Keyword(s):  
Symmetric Space ◽  
Symmetric Spaces ◽  
Riemannian Symmetric Space ◽  
Totally Geodesic Submanifold ◽  
Totally Geodesic ◽  
Geodesic Submanifold ◽  
Riemannian Symmetric Spaces

AbstractLetMbe an irreducible Riemannian symmetric space. The index ofMis the minimal codimension of a (nontrivial) totally geodesic submanifold ofM. We prove that the index is bounded from below by the rank of the symmetric space. We also classify the irreducible Riemannian symmetric spaces whose index is less than or equal to 3.

scholarly journals Brauer equivalent number fields and the geometry of quaternionic Shimura varieties

2018 ◽  
Vol 70 (2) ◽  
pp. 675-687
Author(s):  
Benjamin Linowitz
Keyword(s):  
Symmetric Spaces ◽  
Number Fields ◽  
Shimura Varieties ◽  
Brauer Groups ◽  
Locally Symmetric Spaces ◽  
Totally Geodesic ◽  
Equivalent Number ◽  
Geodesic Surfaces

Abstract Two number fields are said to be Brauer equivalent if there is an isomorphism between their Brauer groups that commutes with restriction. In this paper, we prove a variety of number theoretic results about Brauer equivalent number fields (for example, they must have the same signature). These results are then applied to the geometry of certain arithmetic locally symmetric spaces. As an example, we construct incommensurable arithmetic locally symmetric spaces containing exactly the same set of proper immersed totally geodesic surfaces.

Sign in / Sign up

Export Citation Format

Share Document