𝐿²-index of elliptic operators on locally symmetric spaces of finite volume

1982 ◽  
pp. 129-137 ◽  
Author(s):  
Henri Moscovici
Keyword(s):  
Finite Volume ◽  
Symmetric Spaces ◽  
Elliptic Operators ◽  
Locally Symmetric Spaces

scholarly journals Rigidity of horospherical foliations

1989 ◽  
Vol 9 (1) ◽  
pp. 191-205 ◽  
Author(s):  
Dave Witte
Keyword(s):  
Sectional Curvature ◽  
Finite Volume ◽  
Symmetric Spaces ◽  
Positive Sectional Curvature ◽  
Algebraic Form ◽  
Locally Symmetric Spaces

AbstractM. Ratner's theorem on the rigidity of horocycle flows is extended to the rigidity of horospherical foliations on bundles over finite-volume locally-symmetric spaces of non-positive sectional curvature, and to other foliations of the same algebraic form.

Tubes, Cohomology with Growth Conditions and an Application to the Theta Correspondence

1988 ◽  
Vol 40 (1) ◽  
pp. 1-37 ◽  
Author(s):  
Stephen S. Kudla ◽  
John J. Millson
Keyword(s):  
Finite Volume ◽  
Symmetric Spaces ◽  
Integral Formula ◽  
Growth Conditions ◽  
Harmonic Forms ◽  
Theta Correspondence ◽  
Locally Symmetric Spaces ◽  
Spinor Norm ◽  
Integer Coefficients ◽  
Locally Symmetric Space

In this paper we continue our effort [11], [12], [13], [14] to interpret geometrically the harmonic forms on certain locally symmetric spaces constructed by using the theta correspondence. The point of this paper is to prove an integral formula, Theorem 2.1, which will allow us to generalize the results obtained in the above papers to the finite volume case (the previous papers treated only the compact case). We then apply our integral formula to certain finite volume quotients of symmetric spaces of orthogonal groups. The main result obtained is Theorem 4.2 which is described below. We let (,) denote the bilinear form associated to a quadratic form with integer coefficients of signature (p, q). We assume that the fundamental group Γ ⊂ SO(p, q) of our locally symmetric space is the subgroup of the integral isometries of (,) congruent to the identity matrix modulo some integer N. We assume that N is chosen large enough so that Γ is neat (the multiplicative subgroup of C* generated by the eigenvalues of the elements of Γ has no torsion), Borel [2], 17.1 and that every element in Γ has spinor norm 1, Millson-Raghunathan [15], Proposition 4.1. These conditions are needed to ensure that our cycles Cx (see below) are orientable. The methods we will use apply also to unitary and quaternion unitary locally symmetric spaces, see [13].

scholarly journals Lp spectral theory and heat dynamics of locally symmetric spaces

2010 ◽  
Vol 258 (4) ◽  
pp. 1121-1139 ◽  
Author(s):  
Lizhen Ji ◽  
Andreas Weber
Keyword(s):  
Spectral Theory ◽  
Symmetric Spaces ◽  
Locally Symmetric Spaces
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