Related papers: On the Anomaly Formula for the Cappell-Miller Holo…
We present an explicit formula for the deformation quantization on K\"{a}hler manifolds.
For holomorphic vector bundles over compact K\"ahler manifolds, we establish a formula for the asymptotic slope of the {\alpha}-K-energy associated with the Kahler-Yang-Mills equations.
We study an eigenvalue problem for the Laplacian on a compact K\"{a}hler manifold. Considering the $k$-th eigenvalue $\lambda_{k}$ as a functional on the space of K\"{a}hler metrics with fixed volume on a compact complex manifold, we…
We give an explicit formula for the quaternionic K\"ahler metrics obtained by the HK/QK correspondence. As an application, we give a new proof of the fact that the Ferrara-Sabharwal metric as well as its one-loop deformation is quaternionic…
We proved the existence of supersymmetric Hermitian metrics with torsion on a class of non-Kaehler manifolds.
We give an explicit local formula for any formal deformation quantization, with separation of variables, on a K\"ahler manifold. The formula is given in terms of differential operators, parametrized by acyclic combinatorial graphs.
A classification theorem for nearly K\"ahler manifolds of constant antiholomorphic sectional curvature is proved.
In this paper, complex Hessian equation over K\"ahler manifold was studied. Under the condition that the underline K\"ahler manifold has non-negative holomorphic bisectional curvature, the existence and regularity of the solution was…
We show how affine and projective special K\"ahler manifolds emerge from the structure of quantization. We quantize them and construct natural (wavefunction) representations for the corresponding coherent states. These in turn are shown to…
Given an oriented closed manifold $M$ of odd dimension and a unitary representation $\rho : \pi_1(M) \ra \GL_n(\F)$, we define a Reidemeister torsion, even if the cohomology associated with $\rho$ is not acyclic. As corollaries, we…
We construct new examples of constant scalar curvature K\"{a}hler metrics on suitable resolutions of certain constant scalar curvature K\"{a}hler orbifolds with type I singularities, in the sense of Apostolov--Rollin, along a suborbifold of…
We study the behavior of connections and curvature under the HK/QK correspondence, proving simple formulae expressing the Levi-Civita connection and Riemann curvature tensor on the quaternionic K\"ahler side in terms of the initial…
We give a partial account of some problems concerning cohomological invariants and metric properties of complex non-K\"ahler manifolds.
A holomorphic representation formula for special parabolic hyperspheres is given.
We give an elementary introduction to hyperk\"ahler manifolds, survey some of their interesting properties and some open problems.
Let $X$ be a compact connected strongly pseudoconvex CR manifold of dimension $2n+1, n\ge 1$ with a transversal CR $S^1$-action on $X$. In this paper we introduce the Quillen metric on the determinant line of the Fourier components of the…
In this paper we establish new Bochner-Kodaira formulas with quadratic curvature terms on compact K\"ahler manifolds: for any $\eta\in \Omega^{p,q}(M)$, $$ \left\langle\Delta_{\overline \partial} \eta,\eta\right\rangle =\left\langle…
We propose the Hamiltonian model of ${\cal N}=8$ supersymmetric mechanics on $n-$dimensional special K\"ahler manifolds (of the rigid type).
We explore the structure of invariant measures on compact K\"ahler manifolds with Hamiltonian torus actions. We derive the formula for conditional measures on the orbits of the complex torus and use it to prove a conditional statement about…
Inspired by the work of Boris Vertman on refined analytic torsion for manifolds with boundary, in this paper we extend the construction of the Cappell-Miller analytic torsion to manifolds with boundary. We also compare it with the refined…