Araştırma Makalesi

Ricci Curvatures on Hypersurfaces of Almost Product-like Statistical Manifolds

Cilt: 9 Sayı: 1 30 Nisan 2024
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Ricci Curvatures on Hypersurfaces of Almost Product-like Statistical Manifolds

Öz

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.

Anahtar Kelimeler

Destekleyen Kurum

Scientific and Technological Research Council of Turkey (TÜBİTAK)

Proje Numarası

122F326

Etik Beyan

Bu çalışmanın, özgün bir çalışma olduğunu; çalışmanın hazırlık, veri toplama, analiz ve bilgilerin sunumu olmak üzere tüm aşamalarından bilimsel etik ilke ve kurallarına uygun davrandığımı; bu çalışma kapsamında elde edilmeyen tüm veri ve bilgiler için kaynak gösterdiğimi ve bu kaynaklara kaynakçada yer verdiğim kabul ederek etik görev ve sorumluluklara riayet ettiğimi beyan ederim.

Teşekkür

This study is supported by the Scientific and Technological Research Council of Turkey (TÜBiTAK)

Kaynakça

  1. [1] Chen, B.-Y., "Strings of Riemannian invariants, inequalities, ideal immersions and their applications", In: The Third Pacific Rim Geometry Conference (Seoul 1996), Int. Press, Cambridge MA, 25 (1998) : 7–60.
  2. [2] Chen, B.-Y., "Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions", Glasgow Mathematical Journal 41 (1999) : 33–41.
  3. [3] Chen, B.-Y., "On Ricci curvature of isotropic and Langrangian submanifolds in complex space forms", Archiv der Mathematik (Basel) 74 (2000) : 154–160.
  4. [4] Chen, B.-Y, "Pseudo-Riemannian geometry, δ-invariants and applications", World Scientific (2011).
  5. [5] 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.
  6. [6] Chen B.-Y, Blaga A. M., Vîlcu G-E., "Differential geometry of submanifolds in complex space forms involving δ-invariants", Mathematics 10 (2022): 591.
  7. [7] Akyol M. A., Demir R., Poyraz N. Ö., Vîlcu, G-E., "Optimal inequalities for hemi-slant Riemannian submersions", Mathematics, 10 (2022) : 3993.
  8. [8] 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.

Ayrıntılar

Birincil Dil

İngilizce

Konular

Cebirsel ve Diferansiyel Geometri

Bölüm

Araştırma Makalesi

Erken Görünüm Tarihi

30 Nisan 2024

Yayımlanma Tarihi

30 Nisan 2024

Gönderilme Tarihi

13 Ocak 2024

Kabul Tarihi

5 Mart 2024

Yayımlandığı Sayı

Yıl 2024 Cilt: 9 Sayı: 1

Kaynak Göster

APA
Gülbahar, M., Erkan, E., & Düzgör, M. (2024). Ricci Curvatures on Hypersurfaces of Almost Product-like Statistical Manifolds. Journal of Engineering Technology and Applied Sciences, 9(1), 33-46. https://doi.org/10.30931/jetas.1419021
AMA
1.Gülbahar M, Erkan E, Düzgör M. Ricci Curvatures on Hypersurfaces of Almost Product-like Statistical Manifolds. Journal of Engineering Technology and Applied Sciences. 2024;9(1):33-46. doi:10.30931/jetas.1419021
Chicago
Gülbahar, Mehmet, Esra Erkan, ve Meral Düzgör. 2024. “Ricci Curvatures on Hypersurfaces of Almost Product-like Statistical Manifolds”. Journal of Engineering Technology and Applied Sciences 9 (1): 33-46. https://doi.org/10.30931/jetas.1419021.
EndNote
Gülbahar M, Erkan E, Düzgör M (01 Nisan 2024) Ricci Curvatures on Hypersurfaces of Almost Product-like Statistical Manifolds. Journal of Engineering Technology and Applied Sciences 9 1 33–46.
IEEE
[1]M. Gülbahar, E. Erkan, ve M. Düzgör, “Ricci Curvatures on Hypersurfaces of Almost Product-like Statistical Manifolds”, Journal of Engineering Technology and Applied Sciences, c. 9, sy 1, ss. 33–46, Nis. 2024, doi: 10.30931/jetas.1419021.
ISNAD
Gülbahar, Mehmet - Erkan, Esra - Düzgör, Meral. “Ricci Curvatures on Hypersurfaces of Almost Product-like Statistical Manifolds”. Journal of Engineering Technology and Applied Sciences 9/1 (01 Nisan 2024): 33-46. https://doi.org/10.30931/jetas.1419021.
JAMA
1.Gülbahar M, Erkan E, Düzgör M. Ricci Curvatures on Hypersurfaces of Almost Product-like Statistical Manifolds. Journal of Engineering Technology and Applied Sciences. 2024;9:33–46.
MLA
Gülbahar, Mehmet, vd. “Ricci Curvatures on Hypersurfaces of Almost Product-like Statistical Manifolds”. Journal of Engineering Technology and Applied Sciences, c. 9, sy 1, Nisan 2024, ss. 33-46, doi:10.30931/jetas.1419021.
Vancouver
1.Mehmet Gülbahar, Esra Erkan, Meral Düzgör. Ricci Curvatures on Hypersurfaces of Almost Product-like Statistical Manifolds. Journal of Engineering Technology and Applied Sciences. 01 Nisan 2024;9(1):33-46. doi:10.30931/jetas.1419021