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  • Author or Editor: Karina Olszak x
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At first, a necessary and sufficient condition for a Khler-Norden manifold to be holomorphic Einstein is found. Next, it is shown that the so-called (real) generalized Einstein conditions for Khler-Norden manifolds are not essential since the scalarcurvature of such manifolds is constant. In this context, we study generalized holomorphic Einstein conditions. Using the one-to-one correspondence between Khler-Norden structures and holomorphic Riemannian metrics, we establish necessary and sufficient conditions for Khler-Norden manifolds to satisfy the generalized holomorphic Einstein conditions. And a class of new examples of such manifolds is presented. Finally, in virtue of the obtained results, we mention that Theorems 1 and 2 of H. Kim and J. Kim [10] are not true in general.

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It is proved that every concircularly recurrent manifold must be necessarily a recurrent manifold with the same recurrence form.

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