Some characterizations of three-dimensional trans-Sasakian manifolds admitting η- Ricci solitons and trans-Sasakian manifolds as Kagan subprojective space

• Datum: 2020
• Hauptverfasser: Sarkar, A., Sil, A., Paul, A. K., Саркар, А., Сіл, А., Пауль, А. К.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2020
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/6047
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

UDC 514.7 The object of the present paper is to study three-dimensional trans-Sasakian manifolds admitting $\eta$-Ricci soliton. Actually, we study such manifolds whose Ricci tensor satisfy some special conditions like cyclic parallelity, Ricci semisymmetry, $\phi$-Ricci semisymmetry, after reviewing the properties of second order parallel tensors on such manifolds. We determine the form of Riemann curvature tensor of trans-Sasakian manifolds of dimension greater than three as Kagan subprojective spaces. We also give some classification results of trans-Sasakian manifolds of dimension greater than three as Kagan subprojective spaces.