The asymptotic behavior of the steady gradient Kähler–Ricci soliton of the Taub-NUT type of Apostolov and Cifarelli

Abstract We first determine the asymptotic cone of the steady gradient Kähler–Ricci soliton of the Taub-NUT type constructed by Apostolov and Cifarelli. Then we study a special case and prove that it is an ALF Calabi–Yau metric in a certain sense. Finally, we construct new ALF Calabi–Yau metrics on crepant resolution of its quotients modeled on it using the method of Tian–Yau–Hein.