207 research outputs found
Recent developments of the DDVV Conjecture
In this paper, we give a survey of the recent develpoments of the DDVV
conjecture
On the Geometry of Classifying Spaces and Horizontal Slices
In this paper, we study the local properties of the moduli space of a
polarized Calabi-Yau manifold. Let be a neighborhood of the moduli space.
Then we know the universal covering space of is a smooth manifold.
Suppose is the classifying space of a polarized Calabi-Yau manifold with
the automorphism group . Let be the symmetric space associated with
. Then we proved that the map from to induced by the period map is
a pluriharmonic map. We also give a Kahler metric on , which is called the
Hodge metric. We proved that the Ricci curvature of the Hodge metric is
negative away from zero. We also proved the non-existence of the K\"ahler
metric on the classifying space of a Calabi-Yau threefold which is invariant
under a cocompact lattice of
On the Hodge Metric of the Universal Deformation Space of Calabi-Yau Threefolds
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 the ground state of quantum layers
We provide some new results of the ground state of quantum layers
Remarks on the Bottcher-Wenzel Inequality
In 2005, B\"ottcher and Wenzel raised the conjecture that if are real
square matrices, then , where is
the Frobenius norm. Various proofs of this conjecture were found in the last
few years by several authors. We here give another proof. This proof is highly
conceptual and requires minimal computation. We also briefly discuss related
inequalities, in particular, the classical Chern-do Camo-Kobayashi inequality.Comment: Journal reference adde
On the Lower Order Terms of the Asymptotic Expansion of Zelditch
In this paper, we computed the first three coefficients of the asymptotic
expansion of Zelditch. We also proved that in general, the -th coefficient
is a polynomial of the curvature and its derivative of weight .Comment: 34 page
A Note on Special Kahler Manifolds
We proved a conjecture of D. Freed that there are no non-trivial complete
special Kaehler manifolds.Comment: 3 page
Proof of the normal scalar curvature conjecture
In this paper, we proved the normal scalar curvature conjecture and the
Bottcher-Wenzel conjecture
Gradient estimates of the Yukawa coupling
The paper is related to the classification of special manifolds and
projective special manifolds. One of the result of this paper is that, if the
Weil-Petersson metric on a projective special manifold is complete, then the
Hodge metrc and the Weil-Petersson metrc are equivalent
On the Curvature Tensor of the Hodge Metric of Moduli Space of Polarized Calabi-Yau Threefolds
In this paper, we give an expression and some estimates of the curvature
tensor of the Hodge metric over the moduli space of a polarized Calabi-Yau
threefold. The symmetricity of the Yukawa coupling is also studied. In the last
section of this paper, an extra restriction of the limiting Hodge structure for
the degeneration of Calabi-Yau threefolds is given.Comment: We corrected a typo error in the title and corrected the Journal-re
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