# 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

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## References

SHOWING 1-10 OF 26 REFERENCES

### Geometry and Arithmetic on the Siegel-Jacobi Space

- Mathematics, Philosophy
- 2014

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…

### Smooth Compactification of Locally Symmetric Varieties

- Mathematics
- 1975

Preface to the second edition Preface to the first edition 1. Basics on torus embeddings: examples 2. Polyhedral reduction theory in self-adjoint cones 3. Compactifications of locally symmetric…

### 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…

### Symplectic Geometry

- MathematicsActa Applicandae Mathematicae
- 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…