New classes of statistical manifolds with a complex structure
DOI:
https://doi.org/10.33044/revuma.2989Abstract
We define new classes of statistical manifolds with a complex structure. Motivation for our work is the classification of almost Hermitian manifolds with respect to the covariant derivative of the almost complex structure, obtained by Gray and Hervella in 1980. Instead of the Levi-Civita connection, we use a statistical one and obtain eight classes of Kähler manifolds with the statistical connection. Besides, we give some properties of tensors constructed from covariant derivative of the almost complex structure with respect to the statistical connection. From the obtained properties, further investigation of statistical manifolds is possible.
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