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6 papers · 1 filter
Conformally flat submanifolds in spheres and integrable systems
Neil Donaldson, Chuu-Lian Terng
E. Cartan proved that conformally flat hypersurfaces in S^{n+1} for n>3 have at most two distinct principal curvatures and locally envelop a one-parameter family of (n-1)-spheres.…
On the Geometry of the Orbits of Hermann Actions
Oliver Goertsches, Gudlaugur Thorbergsson
We investigate the submanifold geometry of the orbits of Hermann actions on Riemannian symmetric spaces. After proving that the curvature and shape operators of these orbits commut…
Weil-Petersson geometry on moduli space of polarized Calabi-Yau manifolds
Zhiqin Lu, Xiaofeng Sun
In this paper, we define and study the Weil-Petersson geometry. Under the framework of the Weil-Petersson geometry, we study the Weil-Petersson metric and the Hodge metric. Among t…
On the Hodge Metric of the Universal Deformation Space of Calabi-Yau Threefolds
Zhiqin Lu
In this paper, we represent the Hodge metric in terms of the Weil-Petersson metric and its Ricci curvature on the moduli spaces of polarized Calabi-Yau threefolds.
On K-Stability of Reductive Varieties
Valery Alexeev, Ludmil Katzarkov
G. Tian and S.K. Donaldson formulated a conjecture relating GIT stability of a polarized algebraic variety to the existence of a Kahler metric of constant scalar curvature. In [Don…
Differential geometry via harmonic functions
Peter Li
In this talk, I will discuss the use of harmonic functions to study the geometry and topology of complete manifolds. In my previous joint work with Luen-fai Tam, we discovered that…