Analysis of Total Umbilical Fibers in Riemannian Submersions with Quarter Symmetric Non-Metric Connections
Bibliographic record
Abstract
In this study, we examine the geometric properties of Riemannian submersions with quarter symmetric non-metric connections. Our work provides a compre-hensive analysis of the Weyl projective curvature tensor, the concircular curvature tensor, and the conharmonic curvature tensor. We also investigate how these curvature tensors interact with the total umbilic fibers, particularly focusing on their behavior when such fibers are present in Riemannian submersions. First we introduce basic properties of quarter symmetric non-metric connections. Subse-quently, we compute the relevant curvature tensors and analyze their interplay with total umbilic fibers. In this context, we elucidate relationships between var-ious curvature tensors and certain geometric properties, as well as the effects of these relationships on Riemannian submersions.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.005 | 0.009 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".