Article 2025 · 3 atıf

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

De, Krishnendu, De, Uday chand, Gezer, Aydin

Özet

This article carries out the investigation of a three-dimensional Riemannian manifold N 3 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 N 3 . It is established that a N 3 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 N 3 with the semi-symmetric type non-metric connection is a gradient Yamabe soliton, then either N 3 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 N 3 with a semi-symmetric type non-metric connection whose metrics are Einstein solitons and in-quasi Einstein solitons of gradient type, respectively.

Anahtar Kelimeler

Riemannian manifolds gradient Ricci solitons gradient Yamabe solitons gradient Einstein solitons in-quasi Einstein solitons YAMABE SOLITONS

WoS Kategorileri

Mathematics

Künye

Dergi: KRAGUJEVAC JOURNAL OF MATHEMATICS
Yıl: 2025
Cilt: 49
Sayı: 3
Sayfa: 387-400
ISSN: 1450-9628
DOI: 10.46793/KgJMat2503.387D
WoS UID: WOS:001414979500005

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