Hessian of the Metric Form on Twistor Spaces
نویسنده
چکیده
We compute the hessian iddW of the natural metric form W on the twistor space T(M, g) of a 4-dimensional Riemannian manifold (M, g). We then adapt the computations to the case of the twistor space T(M, g,D) of a hyperkähler manifold (M, g,D = (I, J,K)). We show a strong positivity property of the hessian iddW on the twistor space T(M, g,D) and prove, as an application, a convexity property of the component of the twistor lines in the cycle space of T(M, g,D).
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