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Journals / Journal of Engineering Technology and Applied Sciences / 2026 / Cilt: 9 Sayı: 1

Ricci Curvatures on Hypersurfaces of Almost Product-like Statistical Manifolds

Mehmet Gülbahar(HARRAN ÜNİVERSİTESİ)0000-0001-6950-7633
Esra Erkan(HARRAN ÜNİVERSİTESİ)0000-0003-0456-6418
Meral Düzgör(HARRAN ÜNİVERSİTESİ)0009-0008-7411-1498
Pages
33–46
Publication Date
2024-04-30
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Using the Chen-Ricci inequality, some characterizations are presented.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Riemannian curvature invariants on hypersurfaces of an almost product-like manifold with constant curvature υ are computed.
📊
Key Findings & Data:Various relationships involving sectional curvatures and Ricci curvatures have been obtained.
💡
Conclusion & Impact:Using the Chen-Ricci inequality, some characterizations are presented.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Riemannian curvature invariants · hypersurfaces · product manifolds

Abstract

Riemannian curvature invariants on hypersurfaces of an almost product-like manifold with constant curvature υ are computed. Various relationships involving sectional curvatures and Ricci curvatures have been obtained. Using the Chen-Ricci inequality, some characterizations are presented.

🔖

Cite This Article

Gülbahar, M., Erkan, E., Düzgör, M. (2024). Ricci Curvatures on Hypersurfaces of Almost Product-like Statistical Manifolds. Journal of Engineering Technology and Applied Sciences, Cilt: 9 Sayı: 1, 33–46. https://doi.org/10.30931/jetas.1419021

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  39. Suceava B. D., Vajiac M. B., "Remarks on Chen's fundamental inequality with classical curvature invariants in Riemannian spaces", Analele Stiintifice ale Universitatii Alexandru Ioan Cuza" Din Iasi. Mathematics. (NS) 54 (2008): 27-37.
  40. Akyol M. A., Demir R., Poyraz N. Ö., Vîlcu, G-E., "Optimal inequalities for hemi-slant Riemannian submersions", Mathematics, 10 (2022): 3993.
  41. Özgür C., and Tripathi M. M., "On submanifolds satisfying Chen's equality in a real space form", The Arabian Journal for Science and Engineering 33(2A) (2008): 321-330.
  42. Gülbahar M., Kılıç, E. Keleş, S., "A useful orthonormal basis on bi-slant submanifolds of almost Hermitian manifolds", Tamkang Journal of Mathematics 47(2) (2016): 143-161.
  43. Sarı R., Ünal İ. "On curvatures of semi-invariant submanifolds of Lorentzian para-Sasakian manifolds", Turkish Journal of Mathematics and Computer Science 15(2) (2023): 464-469.
  44. Sun K., Marchand-Maillet S., "An information geometry of statistical manifold learning", Proceedings of the 31st International Conference on Machine Learning (ICML-2014), (2014): 1-9.
  45. Bahadır O., Siddiqui A. N., Gülbahar M., Alkhaldi, A. H., "Main curvatures identities on lightlike hypersurfaces of statistical manifolds and their characterizations", Mathematics 10(13) (2022): 2290.
  46. Erkan, E., Gülbahar, M., "Chen's basic inequalities for hypersurfaces of statistical Riemannian manifolds", International Journal of Maps in Mathematics 6(1) (2023): 37-53.
  47. Erkan, E., Gülbahar, M., "Locally product-like statistical manifolds and their hypersurfaces", International Electronic Journal of Geometry, 16(2) (2023): 435-450.
  48. Kazan S. and Takano K. "Anti-invariant holomorphic statistical submersions", Results in Mathematics 78(128) (2023): 1-18.
  49. Gündüzalp Y., "Semi-slant submersions from almost product Riemannian manifolds", Demonstratio Mathematica 49(3) (2016): 345-356.
  50. Gündüzalp Y., "Anti-invariant Riemannian submersions from almost product Riemannian manifolds", Mathematical Sciences and Applications E-Notes 1(1) (2013): 58-66.
  51. Rahman S., Haseeb A., Almusawa H., "Geometry of warped product pseudo slant submanifolds in a nearly quasi-Sasakian manifold", Italian Journal of Pure and Applied Mathematics, (48) (2022): 1021–1032.
  52. Şahin B., Atçeken M., "Semi-invariant submanifolds of Riemannian product manifold", Balkan Journal of Geometry and its applications 8(1) (2023): 91-100.
  53. Şahin B., "Slant submanifolds of an almost product Riemannian manifold", Journal of the Korean Mathematical Society 43(4) (2006): 717-732.
  54. Opozda B., "A sectional curvature for statistical structures", Linear Algebra and its Applications 497, (2016): 134–161.