Abstract
It is known that a conformal vector field on a compact Kaehler manifold is a Killing vector field. In this paper, we are interested in finding conditions under which a conformal vector field on a non-compact Kaehler manifold is Killing. First we prove that a harmonic analytic conformal vector field on a 2n-dimensional Kaehler manifold (n ≠ 2) of constant nonzero scalar curvature is Killing. It is also shown that on a 2n-dimensional Kaehler Einstein manifold (n > 1) an analytic conformal vector field is either Killing or else the Kaehler manifold is Ricci flat. In particular, it follows that on non-flat Kaehler Einstein manifolds of dimension greater than two, analytic conformal vector fields are Killing.
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This work is supported by the Research Center, College of Science, King Saud University.
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Deshmukh, S. Conformal vector fields on Kaehler manifolds. Ann Univ Ferrara 57, 17–26 (2011). https://doi.org/10.1007/s11565-011-0114-8
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DOI: https://doi.org/10.1007/s11565-011-0114-8
Keywords
- Kaehler manifolds
- Euclidean complex space form
- Ricci curvature
- Analytic vector fields
- Conformal vector field
- Harmonic vector fields