On special Kähler metrics and hypersurfaces

Minimal surfaces in 3-manifolds play an important role in 3-dimensional geometry. In higher dimensions, there are special geometric structures, including Ricci-flat Kähler structures on complex manifolds. They are called Calabi-Yau manifolds. Generalizations include Kähler-Ricci soliton structures. In this dissertation, we study these special Kähler metrics and hypersurfaces in Kähler Ricci-flat spaces. Particularly, we determine the second fundamental form of the sphere inthe Euclidean sense in Eguchi-Hanson spaces, motivated by constructing constant mean curvature hypersurfaces. We quantify how far these spheres are from being umbilic.

Name thesis:degree_name

Ph.D.

Discipline thesis:degree_discipline

Mathematics

Grantor dc:publisher

University of Kansas

Year dc:date.issued

2026

Author dc:creator

• Gong, Sien

Advisor dc:contributor.advisor

• Wang, Yuanqi

• Eguchi-Hanson
• Second Fundamental Form

Language dc:language.iso

en

Dc Identifier Other

https://www.proquest.com/LegacyDocView/DISSNUM/32701256

OAI identifier oai:identifier

oai:kuscholarworks.ku.edu:1808/39470