| Title:
|
Algebraic restrictions on geometric realizations of curvature models (English) |
| Author:
|
Dunn, Corey |
| Author:
|
Smith, Zoë |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
57 |
| Issue:
|
3 |
| Year:
|
2021 |
| Pages:
|
175-194 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We generalize a previous result concerning the geometric realizability of model spaces as curvature homogeneous spaces, and investigate applications of this approach. We find algebraic restrictions to realize a model space as a curvature homogeneous space up to any order, and study the implications of geometrically realizing a model space as a locally symmetric space. We also present algebraic restrictions to realize a curvature model as a homothety curvature homogeneous space up to even orders, and demonstrate that for certain model spaces and realizations, homothety curvature homogeneity implies curvature homogeneity. (English) |
| Keyword:
|
curvature model |
| Keyword:
|
curvature homogeneous |
| Keyword:
|
homothethy curvature homogeneous |
| MSC:
|
15A69 |
| MSC:
|
53B15 |
| MSC:
|
53B30 |
| idZBL:
|
Zbl 07396182 |
| idMR:
|
MR4306176 |
| DOI:
|
10.5817/AM2021-3-175 |
| . |
| Date available:
|
2021-07-30T12:30:20Z |
| Last updated:
|
2021-11-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149020 |
| . |
| Reference:
|
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