Conification construction for Kaehler manifolds and its application in c-projective geometry

Abstract

Two Kaehler metrics on one complex manifold are said to be c-projectively equivalent if their J-planar curves, i.e., curves defined by the property that their acceleration is complex proportional to their velocity, coincide. The degree of mobility of a Kaehler 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 simply connected 2n-dimensional Riemannian Kaehler manifolds. We also describe all such values under the additional assumption that the metric is Einstein. As an application, we describe all possible dimensions of the space of essential c-projective vector fields of Kaehler and Kaehler-Einstein Riemannian metrics. We also show that two c-projectively equivalent Kaehler Einstein metrics (of arbitrary signature) on a closed manifold have constant holomorphic curvature or are affinely equivalent.

References in corpus (2)

• Degree of mobility for metrics of lorentzian signature and parallel (0,2)-tensor fields on cone manifolds
• Four-dimensional Kähler metrics admitting c-projective vector fields

Cited by in corpus (8)

• C-projective geometry
• Projectively related metrics, Weyl nullity, and metric projectively invariant equations
• Submaximally symmetric c-projective structures
• C-Projective Compactification; (quasi--)Kaehler Metrics and CR boundaries
• The degree of mobility of Einstein metrics
• Curvature and the c-projective mobility of Kaehler metrics with hamiltonian 2-forms
• Conformal Killing forms in Kaehler geometry
• The c-projective symmetry algebras of Kähler surfaces