Characterization of Ricci Solitons and Harmonic Vector Fields on the Lie Group <i>Nil</i><sup>4</sup>
This study considers a left-invariant Riemannian metric <i>g</i> on the Lie group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mi>i</mi><msup><mi&...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-03-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/7/1155 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | This study considers a left-invariant Riemannian metric <i>g</i> on the Lie group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mi>i</mi><msup><mi>l</mi><mn>4</mn></msup></mrow></semantics></math></inline-formula>. We introduce a Ricci solitons’ classification on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>N</mi><mi>i</mi><msup><mi>l</mi><mn>4</mn></msup><mo>,</mo><mi>g</mi><mo>)</mo></mrow></semantics></math></inline-formula>. These are expansive non-gradient Ricci solitons. We examine the existence of harmonic maps into <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>N</mi><mi>i</mi><msup><mi>l</mi><mn>4</mn></msup><mo>,</mo><mi>g</mi><mo>)</mo></mrow></semantics></math></inline-formula> from a compact Riemannian manifold. Additionally, we provide a characterization of a class of harmonic vector fields on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>N</mi><mi>i</mi><msup><mi>l</mi><mn>4</mn></msup><mo>,</mo><mi>g</mi><mo>)</mo></mrow></semantics></math></inline-formula>. |
|---|---|
| ISSN: | 2227-7390 |