A Study on ϕ-Ricci Symmetric LP-Sasakian Manifolds
Bibliographic record
Abstract
The present paper is devoted to an in-depth study of ϕ-Ricci symmetric LP-Sasakian manifolds, which represent a significant class of Lorentzian para-Sasakian manifolds with rich geometric structures and distinctive curvature characteristics. The notion of ϕ-Ricci symmetry imposes specific constraints on the Ricci tensor in relation to the structure tensor ϕ, offering deeper insight into the curvature behavior and intrinsic geometry of these manifolds. This investigation aims to explore various fundamental properties of ϕ-Ricci symmetric LP-Sasakian manifolds, examining how these symmetry conditions influence their global and local geometric features. To support and illustrate the theoretical analysis, we construct an explicit example of a three-dimensional ϕ-Ricci symmetric LP-Sasakian manifold. Moreover, we study W1-flat LP-Sasakian manifold.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.008 | 0.011 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".