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Abstract In this paper we construct examples of different types of connections starting from a semi-symmetric metric connection g , for example a connection which is a symmetric metric connection with respect to a conformally related metric, but symmetric non-metric with respect to the initial metric. We formulate an open problem: to find a parallel complex structure on a Kaehler manifold with respect to such a new connection.
Adela Mihai (Wed,) studied this question.
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