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Title: Local normal forms for c-projectively equivalent metrics and proof of the Yano-Obata conjecture in arbitrary signature. Proof of the projective Lichnerowicz conjecture for Lorentzian metrics
Authors: Bolsinov, Alexey V.
Matveev, Vladimir S.
Rosemann, Steffan
Issue Date: 2015
Publisher: arXiv.org
Citation: BOLSINOV, A.V., MATVEEV, V.S. and ROSEMANN, S., 2015. Local normal forms for c-projectively equivalent metrics and proof of the Yano-Obata conjecture in arbitrary signature. Proof of the projective Lichnerowicz conjecture for Lorentzian metrics. arXiv:1510.00275 [math.DG]
Abstract: Two Kähler metrics on a complex manifold are called c-projectively equivalent if their $J$-planar curves coincide. These curves are defined by the property that the acceleration is complex proportional to the velocity. We give an explicit local description of all pairs of c-projectively equivalent Kähler metrics of arbitrary signature and use this description to prove the classical Yano-Obata conjecture: we show that on a closed connected Kähler manifold of arbitrary signature, any c-projective vector field is an affine vector field unless the manifold is CPn with (a multiple of) the Fubini-Study metric. As a by-product, we prove the projective Lichnerowicz conjecture for metrics of Lorentzian signature: we show that on a closed connected Lorentzian manifold, any projective vector field is an affine vector field.
Description: This pre-print was submitted to arXiv on 1 Oct 2015.
Version: Submitted for publication
URI: https://dspace.lboro.ac.uk/2134/19554
Publisher Link: http://arxiv.org/abs/1510.00275
Appears in Collections:Published Articles (Maths)

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