Related papers: Interpolation in non-positively curved K\"ahler ma…

We obtain sharp quantitative Laplacian upper and lower estimates under no assumption on curvatures. As a result, we derive quantitative Laplacian, area and volume comparison theorems for tubes in Riemannian and K\"ahler manifolds under weak…

We prove an open mapping theorem for the topological spaces dual to finitely presented Heyting algebras. This yields in particular a short, self-contained semantic proof of the uniform interpolation theorem for intuitionistic propositional…

We show that any compact quaternionic contact (qc) hypersurfaces in a hyper-K\"ahler manifold which is not totally umbilical has an induced qc structure, locally qc homothetic to the standard 3-Sasakian sphere. We also show that any nowhere…

Building on the theory of noncommutative complex structures, the notion of a noncommutative K\"ahler structure is introduced. In the quantum homogeneous space case many of the fundamental results of classical K\"ahler geometry are shown to…

In this article, we propose the following conjecture: if the Strominger connection of a compact Hermitian manifold has constant non-zero holomorphic sectional curvature, then the Hermitian metric must be K\"ahler. The main result of this…

Compact Hermitian symmetric spaces are K\"ahler manifolds with constant scalar curvature and non-negative sectional curvature. A famous result by A. Gray states that, conversely, a compact simply connected K\"ahler manifold with constant…

In this expository paper we review some twistor techniques and recall the problem of finding compact differentiable manifolds that can carry both K\"ahler and non-K\"ahler complex structures. Such examples were constructed independently by…

In this work, we will verify some comparison results on Kahler manifolds. They are complex Hessian comparison for the distance function from a closed complex submanifold of a Kahler manifold with holomorphic bisectional curvature bounded…

In this note, we discuss the mean curvature flow of graphs of maps between Riemannian manifolds. Special emphasis will be placed on estimates of the flow as a non-linear parabolic system of differential equations. Several global existence…

We show that a statistical manifold manifold of a constant non-zero curvature can be realised as a level line of Hessian potential on a Hessian cone. We construct a Sasakian structure on $TM\times\R$ by a statistical manifold manifold of a…

We study geometry, topology and deformation spaces of noncompact complex hyperbolic manifolds (geometrically finite, with variable negative curvature), whose properties make them surprisingly different from real hyperbolic manifolds with…

We investigate constraints on embeddings of a non-orientable surface in a $4$-manifold with the homology of $M \times I$, where $M$ is a rational homology $3$-sphere. The constraints take the form of inequalities involving the genus and…

For the quantum Heisenberg manifolds, using the action of Heisenberg group we construct a family of spectral triples. It is shown that associated Kasparov module is same for all these spectral triples. Then we show that element is…

In this paper, we prove the integration by parts formula for the non-pluripolar product on a compact K\"ahler manifold. Our result generalizes the special case of potentials with small unbounded loci proved in [BEGZ10].

It is shown that the diameter $\diam (H^1_\mfr(R/I))$ of the first local cohomology module of a tetrahedral curve $C= C(a_1,...,a_6)$ can be explicitly expressed in terms of the $a_i$ and is the smallest non-negative integer $k$ such that…

Using the scalar curvature of the product manifold S^{2}X R and the complete group classification of nonlinear Poisson equation on (pseudo) Riemannian manifolds, we extend the previous results on symmetry analysis of homogeneous wave…

In dimension greater than four, we prove that if a Hermitian non-Kaehler manifold is of pointwise constant antiholomorphic sectional curvatures, then it is of constant sectional curvatures.

In this note we extend a recent result of S. Brendle [3] to Riemannian manifolds with densities and nonnegative Bakry-\'Emery Ricci curvature.

We consider biharmonic maps $\phi:(M,g)\rightarrow (N,h)$ from a complete Riemannian manifold into a Riemannian manifold with non-positive sectional curvature. Assume that $\alpha$ satisfies $1<\alpha<\infty$. If for such an $\alpha$,…

We consider shells in three dimensional Euclidean space which have bounded principal curvatures. We prove Korn's interpolation (or the so called first and a half\footnote{The inequality first introduced in [6]}) and second inequalities on…