Related papers: Differential Geometry of Microlinear Frolicher Spa…
Let M be a manifold endowed with a symmetric affine connection $\Gamma.$ The aim of this paper is to describe a quantization map between the space of second-order polynomials on the cotangent bundle T^{*} M and the space of second-order…
In this paper we construct certain moduli spaces, which we call moduli spaces of (principal) $F$-bundles, and study their basic properties. These spaces are associated to triples consisting of a smooth projective geometrically connected…
The aim of these notes is to describe how to construct canonical bundles of moving frames and differential invariants for parametrized curves in Lagrangian Grassmannians, at least in the monotonic case. Such curves appear as Jacobi curves…
Given a special Kahler manifold M, we give a new, direct proof of the relationship between the quaternionic structure on its cotangent bundle and the variation of Hodge structures on the complexification of TM.
Motivated by the work of Pandey, Ofek, and Shalit on the one hand and deformation theory on the other, we study the Grassmannian of $n$-dimensional multiplier-coinvariant subspaces of the Drury-Arveson space. We show that this space admits…
To every real analytic Riemannian manifold M there is associated a complex structure on a neighborhood of the zero section in the real tangent bundle of M. This structure can be uniquely specified in several ways, and is referred to as a…
The equivalence of a conformal metric on 4-dimensional space-time and a local field of 3-dimensional subspaces of the space of 2-forms over space-time is discussed and the basic notion of transection is introduced. Corresponding relation is…
In this paper, we study rank 2 (quasi) parabolic bundles over the Riemann sphere with an effective divisor and these moduli spaces. First we consider a criterium when a parabolic bundle admits a unramified irregular singular parabolic…
The book is devoted to constructing embedding finite-dimensional maps into trivial bundles and investigating the corresponding general position properties.
Frolicher spaces and smooth mappings form a cartesian closed category. It was shown in our previous paper [Far East Journal of Mathematical Sciences, 35 (2009), 211-233] that its full subcategory of Weil exponentiable Frolicher spaces is…
The general construction of self-adjoint configuration space representations of the Heisenberg algebra over an arbitrary manifold is considered. All such inequivalent representations are parametrised in terms of the topology classes of flat…
In this paper we define and study pseudoholomorphic vector bundles structures, particular cases of which are tangent and normal bundle almost complex structures. These are intrinsically related to the Gromov D-operator. As an application we…
We study closures of GL_2(R)-orbits on the total space of the Hodge bundle over the moduli space of curves under the assumption that they are algebraic manifolds. We show that, in the generic stratum, such manifolds are the whole stratum,…
We show how the formalism of Frobenius descent for torsors enables to study torsors under Frobenius kernels in terms of non-commutative, Lie-valued differential forms. We pay particular attention to affine line bundles trivialized by the…
Consider the nonstandard embedding of SO(3) into SO(5) given by the 5-dimensional irreducible representation of SO(3), henceforth called SO(3)_\ir. In this note, we study the topology and the differential geometry of 5-dimensional…
It is shown that a canonical geometric setting of the integrable TED equation is a Kahlerian tangent bundle of an affine manifold. The remarkable multi-dimensional consistency of this 4+4-dimensional dispersionless partial differential…
The purpose of this paper is to give two supplements for vanishing theorems: One is a relative version of the Kawamata-Viehweg-Nadel type vanishing theorem, which is obtained from an observation for the variation of the numerical dimension…
This paper is an addition to the book [54] on Compact projective planes. Such planes, if connected and finite-dimensional, have a point space of topological dimension 2, 4, 8, or 16, the classical example in the last case being the…
Chern number formulas for holomorphic jet bundles are computed for projective curves and for projective surfaces. These formulas are used to show that certain minimal surfaces of general type (generic hypersurfaces of degree at least 5 in…
In this review the foundations of Geometric Quantization are explained and discussed. In particular, we want to clarify the mathematical aspects related to the geometrical structures involved in this theory: complex line bundles, hermitian…