RICCI-BOURGUIGNON SOLITONS AND FISCHER-MARSDEN CONJECTURE ON GENERALIZED SASAKIAN-SPACE-FORMS WITH β-KENMOTSU STRUCTURE

초록

Our aim is to study the properties of Fischer-Marsden conjecture and Ricci-Bourguignon solitons within the framework of generalized Sasakian-space-forms with beta-Kenmotsu structure. It is proven that a (2n + 1)-dimensional generalized Sasakian-space-form with beta-Kenmotsu structure satisfying the Fischer-Marsden equation is a conformal gradient soliton. Also, it is shown that a generalized Sasakian-space-form with beta-Kenmotsu structure admitting a gradient Ricci-Bourguignon soliton is either psi\T-k xM(2n+1-k) or gradient eta-Yamabe soliton.

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