相关论文: The conformal deformation detour complex for the o…

We give explicit formulas for conformally invariant operators with leading term an $m$-th power of Laplacian on the product of spheres with the natural pseudo-Riemannian product metric for all $m$.

We give a simple construction of the Bernstein-Gelfand-Gelfand sequences of natural differential operators on a manifold equipped with a parabolic geometry. This method permits us to define the additional structure of a bilinear…

Motivated by the Landau-Ginzburg model, we study the Witten deformation on a noncompact manifold with bounded geometry, together with some tameness condition on the growth of the Morse function $f$ near infinity. We prove that the…

A conformal structure on a manifold $M^n$ induces natural second order conformally invariant operators, called M\"obius and Laplace structures, acting on specific weight bundles of $M$, provided that $n\ge 3$. By extending the notions of…

The Fredholm determinants of a special class of integral operators K supported on the union of m curve segments in the complex plane are shown to be the tau-functions of an isomonodromic family of meromorphic covariant derivative operators…

We use the Thom-Whitney construction to show that infinitesimal deformations of a coherent sheaf F are controlled by the differential graded Lie algebra of global sections of an acyclic resolution of the sheaf End(E), where E is any locally…

A section of a Riemannian $G$-manifold $M$ is a closed submanifold $\Sigma$ which meets each orbit orthogonally. It is shown that the algebra of $G$-invariant differential forms on $M$ which are horizontal in the sense that they kill every…

We study Riemannian foliations with complex leaves on Kaehler manifolds. The tensor T, the obstruction to the foliation be totally geodesic, is interpreted as a holomorphic section of a certain vector bundle. This enables us to give…

We study the decomposition of the Riemannian curvature R tensor of an almost quaternion-Hermitian manifold under the action of its structure group Sp(n)Sp(1). Using the minimal connection, we show that most components are determined by the…

Conformal geodesics are distinguished curves on a conformal manifold, loosely analogous to geodesics of Riemannian geometry. One definition of them is as solutions to a third order differential equation determined by the conformal…

Given a complex manifold $X$ and a smooth positive function $\eta$ thereon, we perturb the standard differential operator $d=\partial + \bar\partial$ acting on differential forms to a first-order differential operator $D_\eta$ whose…

We study locally trivial deformations of toric varieties from a combinatorial point of view. For any fan $\Sigma$, we construct a deformation functor $\mathrm{Def}_\Sigma$ by considering \v{C}ech zero-cochains on certain simplicial…

We study compact complex manifolds $M$ admitting a conformal holomorphic Riemannian structure invariant under the action of a complex semi-simple Lie group $G$. We prove that if the group $G$ acts transitively and essentially, then $M$ is…

We consider conformal defects with spins under the rotation group acting on the transverse directions. They are described in the embedding space formalism in a similar manner to spinning local operators, and their correlation functions with…

The curvature discussed in this paper is a rather far going generalization of the Riemannian sectional curvature. We define it for a wide class of optimal control problems: a unified framework including geometric structures such as…

We give manifolds in both the Riemannian and in the higher signature settings whose Riemann curvature operators commute, i.e. which satisfy R(a,b)R(c,d)=R(c,d)R(a,b) for all tangent vectors. These manifolds have global geometric phenomena…

Given a compact Kaehler manifold, we consider the complement U of a divisor with normal crossings. We study the variety of unitary representations of the fundamental group of U with certain restrictions related to the divisor. We show that…

The class of the Riemannian almost product manifolds with nonintegrable structure is considered. Some identities for curvature tensor as certain invariant tensors and quantities are obtained.

An \emph{$\omega$-admissible almost complex structure} on a $2n$-dimensional symplectic manifold $(M,\omega)$ is a $\omega$-calibrated almost complex structure $J$ admitting a nowhere vanishing $\bar{\partial}_J$-closed $(n,0)$-form $\psi$.…

Progress along the line of a previous article are reported. One main point is to include chiral operators with fractional quantum group spins (fourth or sixth of integers) which are needed to achieve modular invariance. We extend the study…