# Problems in the Geometry of the Siegel-Jacobi Space

@article{Yang2019ProblemsIT, title={Problems in the Geometry of the Siegel-Jacobi Space}, author={Jae-Hyun Yang}, journal={arXiv: Differential Geometry}, year={2019} }

The Siegel-Jacobi space is a non-symmetric homogeneous space which is very important geometrically and arithmetically. In this short paper, we propose the basic problems in the geometry of the Siegel-Jacobi space.

## One Citation

A Hall of Statistical Mirrors

- Mathematics
- 2021

The primary objects of study in information geometry are statistical manifolds, which are parametrized families of probability measures, induced with the Fisher-Rao metric and a pair of torsion-free…

## References

SHOWING 1-10 OF 22 REFERENCES

Geometry and Arithmetic on the Siegel–Jacobi Space

- Mathematics
- 2015

The Siegel–Jacobi space is a non–symmetric homogeneous space which is very important geometrically and arithmetically. In this paper, we discuss the theory of the geometry and the arithmetic of the…

SECTIONAL SURVATURES OF THE SIEGEL-JACOBI SPACE

- Mathematics
- 2013

In this paper, we compute the sectional curvatures and the scalar curvature of the Siegel-Jacobi space H1 × C of degree 1 and index 1 explicitly.

Differential operators for Siegel-Jacobi forms

- Mathematics
- 2013

For any positive integers n and m, Hn,m:= Hn ×C(m,n) is called the Siegel-Jacobi space, with the Jacobi group acting on it. The Jacobi forms are defined on this space. We compute the Chern connection…

Groups and geometric analysis

- Mathematics
- 1984

Geometric Fourier analysis on spaces of constant curvature Integral geometry and Radon transforms Invariant differential operators Invariants and harmonic polynomials Spherical functions and…

Siegel's Modular Forms and Dirichlet Series: Course Given at the University of Maryland, 1969 - 1970

- Mathematics
- 1971

Preliminary remarks on topological groups.- Automorphism groups of bilinear forms.- Geometry in the representation space.- Symplectic geometry.- Weakly symmetric Riemannian spaces.- The Riemannian…

Symplectic Geometry

- Mathematics
- 1992

These are lecture notes for two courses, taught at the University of Toronto in Spring 1998 and in Fall 2000. Our main sources have been the books " Symplectic Techniques " by Guillemin-Sternberg and…

SPECTRAL THEORY OF THE LAPLACIAN ON THE MODULAR JACOBI GROUP MANIFOLD

- Mathematics
- 2011

The reduced modular Jacobi group is a semidirect product of SL2(Z) with the lattice Z2. We develop the spectral theory of the invariant Laplacian L on the associated group manifold. The operator L is…

Snapshots of Modern Mathematics from Oberwolfach: Special Values of Zeta Functions and Areas of Triangles

- Mathematics
- 2015

In this snapshot we give a glimpse of the interplay of special values of zeta functions and volumes of triangles. Special values of zeta functions and their generalizations arise in the computation…

The singularities of the invariant metric on the Jacobi line bundle

- Mathematics
- 2016

A theorem by Mumford implies that every automorphic line bundle on a pure open Shimura variety, equipped with an invariant smooth metric, can be uniquely extended as a line bundle on a toroidal…

The characters of semisimple Lie groups

- Mathematics
- 1956

is of the trace class and the mapping Tr:f—*sp(ir(f)) is a distribution on G which is called the character of ir (see [6(d)]). In this paper we shall obtain some results on these characters. Let / be…