Abstract.
We classify and characterize an almost Hermitian manifold M admitting a holomorphically planar conformal vector (HPCV) field (a generalization of a closed conformal vector field) V . We show that if V is nowhere vanishing and strictly non-geodesic, then it is homothetic and almost analytic. If, in addition,M satisfies Gray’s first condition, then M is Kaehler. For a semi-Kaehler manifold M admitting an HPCV field V we show that either V is closed, or M becomes almost Kaehler and V is homothetic and almost analytic.
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Part of this work was done by the second author while he was visiting Sri Sathya Sai Institute Of Higher Learning, Prasanthinilayam, India.
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Ghosh, A., Sharma, R. Almost Hermitian manifolds admitting holomorphically planar conformal vector fields. J. geom. 84, 45–54 (2006). https://doi.org/10.1007/s00022-005-0021-1
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DOI: https://doi.org/10.1007/s00022-005-0021-1