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

Key Points

• The research aims to explore the asymptotic cone and properties of steady gradient Kähler–Ricci solitons of the Taub-NUT type.
• Determined the asymptotic cone of Kähler–Ricci solitons
• Examined a specific case to establish ALF Calabi–Yau properties
• Constructed new ALF Calabi–Yau metrics through Tian–Yau–Hein methods
• Successfully identified the asymptotic cone of the soliton
• Demonstrated a specific case behaving as an ALF Calabi–Yau metric
• Developed new metrics on crepant resolutions modeled after the examined soliton