Paired Statistical Solitons and Torse-Forming Rigidity on Statistical Manifolds
- 1Department of Mathematics, University of Zanjan, Zanjan 45371-38791, Iran
- 2Unit of Sciences and Mathematics, Department of Supportive Requirements, University of Technology and Applied Sciences, P.O. Box 77, Shinas 324, Oman
- 3Department of Mathematics, Jamia Millia Islamia, New Delhi 110025, India
Abstract
We study paired statistical η-Ricci–Bourguignon almost solitons on a statistical manifold endowed with two dual torsion-free statistical connections. The same potential field is required to satisfy compatible soliton equations for both connections. By adding and subtracting these equations, we obtain identities that separate the Levi–Civita contribution from the cubic tensor associated with the statistical difference tensor. We distinguish the connection-induced symmetric deformation tensor from the ordinary Lie derivative and derive sum and difference identities that isolate the cubic tensor associated with the statistical difference tensor. We prove a spanning-family criterion for full collapse of the dual connections and derive corresponding gradient η-Ricci–Bourguignon and gradient Schouten identities. Explicit affine and Fisher-geometric examples show non-vacuity and exhibit K≠0 together with K(X,·)=0. A Lorentzian perfect-fluid formulation and an exact FLRW-type realization illustrate how the geometric equations enter relativistic models. The mathematical conclusions are separated from model-dependent physical interpretations.
Related
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BibTeX
@article{balgeshir2026paired,
title = {{Paired Statistical Solitons and Torse-Forming Rigidity on Statistical Manifolds}},
author = {Mohammad Bagher Kazemi Balgeshir and Sudhakar Kumar Chaubey and Mohammad Hasan Shahid},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14213964},
url = {https://www.mdpi.com/2227-7390/14/21/3964},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Paired Statistical Solitons and Torse-Forming Rigidity on Statistical Manifolds
AU - Mohammad Bagher Kazemi Balgeshir
AU - Sudhakar Kumar Chaubey
AU - Mohammad Hasan Shahid
PY - 2026
DA - 2026/10/30
JO - Mathematics
DO - 10.3390/math14213964
UR - https://www.mdpi.com/2227-7390/14/21/3964
AB - We study paired statistical η-Ricci–Bourguignon almost solitons on a statistical manifold endowed with two dual torsion-free statistical connections. The same potential field is required to satisfy compatible soliton equations for both connections. By adding and subtracting these equations, we obtain identities that separate the Levi–Civita contribution from the cubic tensor associated with the statistical difference tensor. We distinguish the connection-induced symmetric deformation tensor from the ordinary Lie derivative and derive sum and difference identities that isolate the cubic tensor associated with the statistical difference tensor. We prove a spanning-family criterion for full collapse of the dual connections and derive corresponding gradient η-Ricci–Bourguignon and gradient Schouten identities. Explicit affine and Fisher-geometric examples show non-vacuity and exhibit K≠0 together with K(X,·)=0. A Lorentzian perfect-fluid formulation and an exact FLRW-type realization illustrate how the geometric equations enter relativistic models. The mathematical conclusions are separated from model-dependent physical interpretations.
SN - 2227-7390
ER -