Abstract
Let \(F:=\alpha +|\beta |\) be a strong Randers metric on a complex manifold. We show that \(F\) is Kähler if and only if \(\beta \) is parallel with respect to \(\alpha \). Furthermore if \(\alpha \) has constant holomorphic sectional curvature, we show that the following assertions are equivalent: (i) \(F\) is Kähler; (ii) \(F=|v|^{2}+\langle c,\bar{v}\rangle \) is a Minkowskian metric unless \(F\) is usually Kählerian.
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Acknowledgments
This work is supported by the National Natural Science Foundation of China 11371032 and the Doctoral Program of Higher Education of China 20110001110069. Second author is supported by the doctoral scientific research foundation of Henan Normal University 01016500130.
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Mo, X., Zhu, H. Some results on strong Randers metrics. Period Math Hung 71, 24–34 (2015). https://doi.org/10.1007/s10998-014-0082-8
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DOI: https://doi.org/10.1007/s10998-014-0082-8