INVESTIGATIONS ON A RIEMANNIAN MANIFOLD WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION AND GRADIENT SOLITONS

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De K., De U. C., GEZER A.

Kragujevac Journal of Mathematics, cilt.49, sa.3, ss.387-400, 2025 (ESCI)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 49 Sayı: 3
• Basım Tarihi: 2025
• Doi Numarası: 10.46793/kgjmat2503.387d
• Dergi Adı: Kragujevac Journal of Mathematics
• Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
• Sayfa Sayıları: ss.387-400
• Anahtar Kelimeler: gradient Einstein solitons, gradient Ricci solitons, gradient Yamabe solitons, m-quasi Einstein solitons, Riemannian manifolds
• Atatürk Üniversitesi Adresli: Evet

Özet

This article carries out the investigation of a three-dimensional Riemannian manifold N3 endowed with a semi-symmetric type non-metric connection. Firstly, we construct a non-trivial example to prove the existence of a semi-symmetric type non-metric connection on N3. It is established that a N3 with the semi-symmetric type non-metric connection, whose metric is a gradient Ricci soliton, is a manifold of constant sectional curvature with respect to the semi-symmetric type non-metric connection. Moreover, we prove that if the Riemannian metric of N3 with the semi-symmetric type non-metric connection is a gradient Yamabe soliton, then either N3 is a manifold of constant scalar curvature or the gradient Yamabe soliton is trivial with respect to the semi-symmetric type non-metric connection. We also characterize the manifold N3 with a semi-symmetric type non-metric connection whose metrics are Einstein solitons and m-quasi Einstein solitons of gradient type, respectively.