# PSEUDORIEMANNIAN 2-STEP NILPOTENT LIE GROUPS

@article{Cordero1999PSEUDORIEMANNIAN2N, title={PSEUDORIEMANNIAN 2-STEP NILPOTENT LIE GROUPS}, author={Luis A. Cordero and Phillip. E. Parker}, journal={arXiv: Differential Geometry}, year={1999} }

We begin a systematic study of these spaces, initially following along the lines of Eberlein's comprehensive study of the Riemannian case. In particular, we integrate the geodesic equation, discuss the structure of the isometry group, and make a study of lattices and periodic geodesics. Some major dierences from the Riemannian theory appear. There are many at groups (

## 18 Citations

### LATTICES AND PERIODIC GEODESICS IN PSEUDORIEMANNIAN 2-STEP NILPOTENT LIE GROUPS

- Mathematics
- 2008

We give a basic treatment of lattices Γ in these groups. Certain tori TF and TB provide the model fiber and the base for a submersion of Γ\N. This submersion may not be pseudoriemannian in the usual…

### Lorentz Geometry of 2-Step Nilpotent Lie Groups

- Mathematics
- 2003

We study the geometry of 2-step nilpotent Lie groups endowed with left-invariant Lorentz metrics. After integrating explicitly the geodesic equations, we discuss the problem of the existence of…

### PseudoH-type 2-step nilpotent Lie groups

- Mathematics
- 2003

PseudoH-type is a natural generalization of H-type to geometries with indefinite metric tensors. We give a complete determination of the conjugate locus including multiplicities. We also obtain a…

### Conjugate Loci of Pseudo-Riemannian 2-Step Nilpotent Lie Groups with Nondegenerate Center

- Mathematics
- 2003

We determine the complete conjugate locus along all geodesics parallel or perpendicular to the center (Theorem 2.3). When the center is one-dimensional we obtain formulas in all cases (Theorem 2.5),…

### Pseudo-Riemannian Lie groups of modified H-type

- Mathematics
- 2021

We define a class of Riemannian and pseudo-Riemannian 2-step nilpotent Lie groups with nondegenerate centers (Definition 2.2) that generalize the H-type groups of Kaplan [8, 9, 10]. Examples are…

### Pseudo H-type 2-step Nilpotent Lie Groups

- Mathematics
- 2005

Pseudo H-type is a natural generalization of H-type to geometries with indefinite metric tensors. We give a complete determination of the conjugate locus including multiplicities. We also obtain a…

### Nilsolitons of H-type in the Lorentzian setting

- Mathematics
- 2015

It is known that all left-invariant pseudo-Riemannian metrics onH3 are algebraic Ricci solitons. We consider generalizations of RiemannianH-type, namely pseudoH-type and pH-type. We study algebraic…

### Pseudoriemannian Nilpotent Lie Groups

- Mathematics
- 2006

This is a survey article with a limited list of references (as required by the publisher) which appears in the Encyclopedia of Mathematical Physics, eds. J.-P. Francoise, G.L. Naber and Tsou S.T.…

### On the Existence of a Codimension 1 Completely Integrable Totally Geodesic Distribution on a Pseudo-Riemannian Heisenberg Group

- Mathematics
- 2010

In this note we prove that the Heisenberg group with a left-invariant pseudo- Riemannian metric admits a completely integrable totally geodesic distribution of codimen- sion 1. This is on the…

### The timelike cut locus and conjugate points in Lorentz 2-step nilpotent Lie groups

- Mathematics
- 2004

Abstract.We investigate the timelike cut locus and the locus of conjugate points in Lorentz 2-step nilpotent Lie groups. For these groups with a timelike center, we give some criteria for the…

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We find the Riemann curvature tensors of all leftinvariant Lorentzian metrics on 3-dimensional Lie groups. MSC(1991): Primary 53C50; Secondary 53B30, 53C30. −−−−−−−−−−−−−−−−−−−−−−−−−−→Υ·…

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