A complete parameter classification of left-invariant Bott affine Ricci solitons for two rotated distributions on three-dimensional Lorentzian Lie groups

We classify all left-invariant affine Ricci solitons associated with the Bott connections of two fixed rank-two distributions on the seven standard families of three-dimensional Lorentzian Lie groups. The distributions are defined by a fixed orthogonal change of the spacelike frame. A universal adapted-frame calculation provides explicit connection matrices, curvature operators and the symmetrized Ricci tensor. The equation in the orthogonal-complement direction forces every left-invariant solution to be steady. The remaining equations yield elementary parameter families and finitely many real algebraic branches: four normalized branches for $G_2$, six branches for each sign parameter in $G_4$, and two quartic branches in $G_7$ in addition to its elementary families. Resultants, subresultants, exact polynomial reduction and Sturm root isolation establish necessity, sufficiency and exhaustiveness. Degenerate cases are treated separately, including all families with nonunique soliton vector fields. An invertible frame transformation relates the two distribution problems. The classification is in the stated structure parameters; no quotient by isometries, automorphisms or scaling is taken.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-26
DOI
https://doi.org/10.48550/arxiv.2610.34835
Primary Topic
Advanced Differential Geometry Research
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
preprint

A complete parameter classification of left-invariant Bott affine Ricci solitons for two rotated distributions on three-dimensional Lorentzian Lie groups

Fanqi Lin
arXiv (Cornell University)
Advanced Differential Geometry Research
preprint

A complete parameter classification of left-invariant Bott affine Ricci solitons for two rotated distributions on three-dimensional Lorentzian Lie groups

Fanqi Lin
preprint en

Abstract

We classify all left-invariant affine Ricci solitons associated with the Bott connections of two fixed rank-two distributions on the seven standard families of three-dimensional Lorentzian Lie groups. The distributions are defined by a fixed orthogonal change of the spacelike frame. A universal adapted-frame calculation provides explicit connection matrices, curvature operators and the symmetrized Ricci tensor. The equation in the orthogonal-complement direction forces every left-invariant solution to be steady. The remaining equations yield elementary parameter families and finitely many real algebraic branches: four normalized branches for $G_2$, six branches for each sign parameter in $G_4$, and two quartic branches in $G_7$ in addition to its elementary families. Resultants, subresultants, exact polynomial reduction and Sturm root isolation establish necessity, sufficiency and exhaustiveness. Degenerate cases are treated separately, including all families with nonunique soliton vector fields. An invertible frame transformation relates the two distribution problems. The classification is in the stated structure parameters; no quotient by isometries, automorphisms or scaling is taken.

arXiv (Cornell University)
Advanced Differential Geometry Research
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Laika access coming soon
A complete parameter classification of left-invariant Bott affine Ricci solitons for two rotated distributions on three-dimensional Lorentzian Lie groups — Fanqi Lin · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS