ON ϵ–PARA SASAKIAN MANIFOLDS ADMITTING ∗–CONFORMAL η–RICCI SOLITONS

Öz

This paper characterizes $\epsilon$--para Sasakian manifolds admitting a $*$--conformal $\eta$--Ricci soliton. We analyze solitons under diverse geometric conditions, namely, generalized Ricci recurrence, flatness of specific $\mathcal{W}_i$--curvature tensors ($i=6,7,8$), and $\phi$--$\mathcal{W}_j$--semisymmetry ($j=3,5$). Cases satisfying $Q \cdot R=0$ and $\phi$--Ricci symmetry are also investigated. The study concludes with an explicit 5-dimensional example proving the soliton's existence.

Anahtar Kelimeler

• $\epsilon$--para Sasakian manifolds
• generalized $\eta$--Einstein manifolds
• $\eta$--Einstein manifolds
• conformal curvature tensor

ON ϵ–PARA SASAKIAN MANIFOLDS ADMITTING ∗–CONFORMAL η–RICCI SOLITONS

Öz

Bu makale, $*$-konformal $\eta$-Ricci solitonuna izin veren $\epsilon$--para Sasakian manifoldlarını karakterize etmektedir. Solitonları, genelleştirilmiş Ricci tekrarlaması, belirli $\mathcal{W}_i$--eğrilik tensörlerinin düzlüğü ($i=6,7,8$) ve $\phi$--$\mathcal{W}_j$--yarısimetri ($j=3,5$) gibi çeşitli geometrik koşullar altında analiz ediyoruz. $Q \cdot R=0$ ve $\phi$--Ricci simetrisini sağlayan durumlar da incelenmektedir. Çalışma, solitonun varlığını kanıtlayan açık bir 5 boyutlu örnekle sonuçlanmaktadır.

Anahtar Kelimeler

• $*$--uyumlu $\eta$--Ricci solitons
• $\epsilon$--sasakian için manifoldlar
• genelleştirilmiş $\eta$--Einstein manifoldları
• $\eta$--Einstein manifoldları
• uyumlu eğrilik tensörü

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