arXiv subjects

Mohammad Aqib

Publications and source records attributed to Mohammad Aqib.

7 recordsLinked to original sources

arXiv2026

Non-compact Ricci Solitons of Finite Volume with Potential Field of Constant Length

We study non-compact Ricci solitons of finite volume whose potential vector field has constant length. Under the assumptions that the scalar curvature is constant along the integral curves of the potential field and that a natural divergence term is integrable on the unit tangent bundle, we prove that such Ricci solitons are necessarily trivial. As applications, we obtain rigidity and non-existence results for Ricci solitons whose potential field is the Reeb vector field of almost contact metric and almost $\alpha$-cosymplectic manifolds. In dimension three, we derive consequences for almost $\alpha$-cosymplectic and contact metric manifolds, and we compare our results with the classification of homogeneous almost $\alpha$-cosymplectic Ricci solitons due to Li and Liu. Several examples and non-examples are included to illustrate the necessity of the finite-volume and sign assumptions.

math.DG↗

arXiv2026

Almost Ricci--Bourguignon Solitons on Contact Metric Three-Manifolds

We investigate almost Ricci--Bourguignon solitons on three-dimensional contact metric manifolds. Under natural curvature assumptions, we show that the additional freedom introduced by allowing the soliton function to vary is rigidly constrained by the contact geometry. Using a local orthonormal $\varphi$-basis on the non-Sasakian region, we derive the full component form of the almost Ricci--Bourguignon soliton equation. As applications, we consider the cases where the potential vector field is pointwise collinear with, or orthogonal to, the Reeb vector field. For contact metric three-manifolds satisfying $Q\xi=\sigma\xi$, we prove that a collinear potential field must vanish on the non-Sasakian region whenever $\xi(\sigma)=0$. In the orthogonal case, when $\sigma$ is constant and the manifold is non-Sasakian, the almost soliton function is forced to be constant; hence the soliton reduces to a Ricci--Bourguignon soliton. In fact, the metric is Einstein, and if the orthogonal potential field is not identically zero, then the metric is flat.

math.DG↗

arXiv2026

Mixed Killing Vector Fields on Cigar Ricci-Bourguignon Solitons

In this article, we study mixed Killing vector fields, defined by the condition $L_V L_V g = f\,L_V g$, on Cigar Ricci--Bourguignon solitons. While conformal vector fields are always mixed Killing, the converse fails in flat and open cylinders with base manifold geometries, where the mixed Killing class is infinite-dimensional. We establish a rigidity phenomenon for Cigar Ricci--Bourguignon solitons: any complete steady almost gradient Ricci--Bourguignon soliton on a surface with positive curvature is, up to homothety, Hamilton's Cigar soliton. We then characterise complete mixed Killing fields and show that locally any mixed Killing field is the sum of a rotational Killing field and a mixed Killing radial field. Finally, we establish that the dimension of the vector space of complete mixed Killing fields of Cigar Ricci--Bourguignon solitons is $5$. Moreover, we explicitly determine a basis. Our results show that Cigar Ricci--Bourguignon solitons exhibit behaviour completely different from that of Euclidean space. Finally, we provide a complete description of the geodesic structure of Cigar Ricci--Bourguignon solitons.

math.DG↗

arXiv2026

Finite Volume Einstein Finsler Warped Product Manifolds of Non-positive or Non-negative Scalar Curvature

The notion of warped product plays an important role in Riemannian geometry moreover in geodesic metric spaces. The warped product was first introduced by Bishop and O'Neill to study Riemannian manifolds of negative curvature.Warped products have been mainly used to construct new examples of Riemannian manifolds with prescribed curvature conditions. This construction can be extended for Finslerian metrics with some minor restrictions. This is motivated by Asanov's papers, where some models of relativity theory are described through the warped product of Finsler metrics. These metrics are in the form of $(α,β)$-metrics, which are the generalization of the Randers metrics; which are being asymmetric Finsler metrics in four-dimensional space-time. The product was later extended to the warped product case of Finsler manifolds by the work of Kozma, Peter and Verge.

math.DG↗

arXiv2025

Characterizations of Almost Ricci Bourguignon Solitons

In this paper, we revisit the study of almost Ricci-Bourguignon solitons by clarifying their position in the broader context of Einstein-type metrics. Motivated by known rigidity results for compact almost Ricci solitons, we aim to identify conditions under which a compact almost RB-soliton is trivial or exhibits special geometric properties. We compare our results with classical theorems of Barros and Ribeiro, and explain explicitly how our work extends or complements these earlier findings.

math.DG↗

arXiv2025

Table Comprehension in Building Codes using Vision Language Models and Domain-Specific Fine-Tuning

Building codes contain critical information for ensuring safety, regulatory compliance, and informed decision-making in construction and engineering. Automated question answering systems over such codes enable quick and accurate access to specific regulatory clauses, improving efficiency and reducing errors. Retrieval-Augmented Generation (RAG) systems are essential for this task as they combine the precision of information retrieval with the generative capabilities of language models. However, tabular data are challenging to extract as they often involve complex layouts, merged cells, multi-row headers, and embedded semantic relationships that are not easily captured by traditional natural language processing techniques and Vision Language Models (VLMs). This paper explores and compares two methods for extracting information from tabular data in building codes using several pre-trained VLMs. First, a direct input method is used, where the image of the page is input directly into the VLMs, which are then tasked with answering questions based on the image. Second, an indirect input method is introduced, which involves converting an image of a page containing tables into the LaTeX code and then answering inquires based on the LaTeX-based input. The experiments find that the direct input method generally resulted in higher accuracy than the indirect input method. To further improve the performance, we fine-tuned each VLM using Low Rank Adaptation (LoRA) on a domain-specific tabular dataset. The fine-tuned models exhibited substantial improvements, with Qwen2.5-VL-3B-Instruct achieving relative accuracy gains exceeding 100%. Our results highlight the potential of parameter-efficient fine-tuning methods to adapt powerful VLMs for understanding complex structured data in specialized fields, such as building code interpretation and regulatory compliance.

cs.CL↗

arXiv2025

Fine-Tuning Large Language Models and Evaluating Retrieval Methods for Improved Question Answering on Building Codes

Building codes are regulations that establish standards for the design, construction, and safety of buildings to ensure structural integrity, fire protection, and accessibility. They are often extensive, complex, and subject to frequent updates, making manual querying challenging and time-consuming. Key difficulties include navigating large volumes of text, interpreting technical language, and identifying relevant clauses across different sections. A potential solution is to build a Question-Answering (QA) system that answers user queries based on building codes. Among the various methods for building a QA system, Retrieval-Augmented Generation (RAG) stands out in performance. RAG consists of two components: a retriever and a language model. This study focuses on identifying a suitable retriever method for building codes and optimizing the generational capability of the language model using fine-tuning techniques. We conducted a detailed evaluation of various retrieval methods by performing the retrieval on the National Building Code of Canada (NBCC) and explored the impact of domain-specific fine-tuning on several language models using the dataset derived from NBCC. Our analysis included a comparative assessment of different retrievers and the performance of both pre-trained and fine-tuned models to determine the efficacy and domain-specific adaptation of language models using fine-tuning on the NBCC dataset. Experimental results showed that Elasticsearch proved to be the most robust retriever among all. The findings also indicate that fine-tuning language models on an NBCC-specific dataset can enhance their ability to generate contextually relevant responses. When combined with context retrieved by a powerful retriever like Elasticsearch, this improvement in LLM performance can optimize the RAG system, enabling it to better navigate the complexities of the NBCC.

cs.CL↗