SURFACES OBTAINED FROM ℂP<sup>N-1</sup> SIGMA MODELS
Bibliographic record
Abstract
In this paper, the Weierstrass technique for harmonic maps S2 → ℂPN-1 is employed in order to obtain surfaces immersed in multidimensional Euclidean spaces. It is shown that if the ℂPN-1 model equations are defined on the sphere S2 and the associated action functional of this model is finite, then the generalized Weierstrass formula for immersion describes conformally parametrized surfaces in the su (N) algebra. In particular, for any holomorphic or antiholomorphic solution of this model the associated surface can be expressed in terms of an orthogonal projector of rank (N - 1). The implementation of this method is presented for two-dimensional conformally parametrized surfaces immersed in the su (3) algebra. The usefulness of the proposed approach is illustrated with examples, including the dilation-invariant meron-type solutions and the Veronese solutions for the ℂP2 model. Depending on the location of the critical points (zeros and poles) of the first fundamental form associated with the meron solution, it is shown that the associated surfaces are semiinfinite cylinders. It is also demonstrated that surfaces related to holomorphic and mixed Veronese solutions are immersed in ℝ8 and ℝ3, respectively.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".