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Öğe Fischer-Marsden conjecture on K-paracontact manifolds and quasi-para-Sasakian manifolds(Ankara Univ, Fac Sci, 2025) Ozkan, Mustafa; Erken, Irem K. U. P. E. L. I.The aim of this paper is to study of the non-trivial solutions of Fischer-Marsden conjecture on K-paracontact manifolds and 3-dimensional quasi-para-Sasakian manifolds. We prove that if a semi- Riemannian manifold of dimension 2n + 1 admits a non-trivial solution of Fischer-Marsden equation, then it has constant scalar curvature. We give a comprehensive classification for a (2n + 1)-dimensional K-paracontact manifold which admits a non-trivial solution of Fischer-Marsden equation. We consider 3-dimensional quasi-para-Sasakian manifolds with beta constant which admits Fischer-Marsden equation and prove that there are two possibilities. The first one is the scalar curvature r = -6 beta 2 and M3 is Einstein. The second one is the manifold is paracosymplectic manifold and eta-Einstein.
