13 citations · 46 across the 12 of their papers we have counts for
12 papers
Nilsolitons of H-type in the Lorentzian setting
Kensuke Onda, Phillip E. Parker
It is known that all left-invariant pseudo-Riemannian metrics on are algebraic Ricci solitons. We consider generalizations of Riemannian -type, namely pseudo-type and $…
Horizontal Path Lifting for General Connections
Phillip E. Parker, Justin M. Ryan
We characterize the existence of horizontal path lifts for general connections on arbitrary fiber bundles with a new property that also gives fresh insight into linear and -conn…
Lattices and Periodic Geodesics in Pseudoriemannian 2-step Nilpotent Lie Groups
Luis A. Cordero, Phillip E. Parker
We give a basic treatment of lattices in these groups. Certain tori and provide the model fiber and the base for a submersion of . This submersion ma…
General Connections, Exponential Maps, and Second-order Differential Equations
L. Del Riego, Phillip. E. Parker
The main purpose of this article is to introduce a comprehensive, unified theory of the geometry of all connections. We show that one can study a connection via a certain, closely…
Pseudoriemannian Nilpotent Lie Groups
Phillip E. Parker
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. Nabe…
PseudoH-type 2-step nilpotent Lie groups
C. Jang, K. Park, P. E. Parker
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. W…