Conification construction for Kähler manifolds and its application in c-projective geometry |
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Authors: | Vladimir S Matveev Stefan Rosemann |
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Institution: | Institute of Mathematics, Friedrich-Schiller-Universität Jena, 07737, Germany |
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Abstract: | Two Kähler metrics on a complex manifold are called c-projectively equivalent if their J -planar curves coincide. Such curves are defined by the property that the acceleration is complex proportional to the velocity. The degree of mobility of a Kähler metric is the dimension of the space of metrics that are c-projectively equivalent to it. We give the list of all possible values of the degree of mobility of a simply connected Kähler manifold by reducing the problem to the study of parallel Hermitian (0,2)-tensors on the conification of the manifold. We also describe all such values for a Kähler–Einstein metric. We apply these results to describe all possible dimensions of the space of essential c-projective vector fields of Kähler and Kähler–Einstein metrics. We also show that two c-projectively equivalent Kähler–Einstein metrics (of arbitrary signature) on a closed manifold have constant holomorphic curvature or are affinely equivalent. |
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Keywords: | Kä hler metrics Conification construction Hamiltonian 2-forms Conformal Killing forms |
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