Related papers: On the Cartan Model of the Canonical Vector Bundle…

A natural explicit condition is given ensuring that an action of the multiplicative monoid of non-negative reals on a manifold F comes from homotheties of a vector bundle structure on F, or, equivalently, from an Euler vector field. This is…

We show that any contact form whose Fefferman metric admits a nonzero parallel vector field is pseudo-Einstein of constant pseudohermitian scalar curvature. As an application we compute the curvature groups of the total space of the…

We study certain moduli spaces of stable vector bundles of rank two on cubic and quartic threefolds. In many cases under consideration, it turns out that the moduli space is complete and irreducible and a general member has vanishing…

Let $X$ be a smooth irreducible projective curve with an involution $\sigma$. A vector bundle $E$ over $X$ is called anti-invariant if there exists an isomorphism $\sigma^*E\rightarrow E^*$. In this paper, we give a construction of the…

With each resonance of the Laplacian acting on the compactly supported sections of a homogeneous vector bundle over a Riemannian symmetric space of the non-compact type, One can associate a residue representation. The purpose of this paper…

We show that intersection numbers on the moduli space of stable bundles of coprime rank and degree over a smooth complex curve can be recovered as highest-degree asymptotics in formulas of Vafa-Intriligator type. In particular, we…

We describe the compact Lorentzian $3$-manifolds admitting a parallel lightlike vector field. The classification of compact Lorentzian $3$-manifolds admitting non-isometric affine diffeomorphisms follows, together with the complete…

We describe the (complex) quaternionic geometry encoded by the embeddings of the Riemann sphere, with nonnegative normal bundles.

We introduce a notion of regularity for coherent sheaves on Grassmannians of lines. We use this notion to prove some extension of Evans-Griffith criterion to characterize direct sums of line bundles. We also give a cohomological…

We study Ulrich bundles and their moduli on unnodal Enriques surfaces. In particular, we prove that unnodal Enriques surfaces are of wild representation type by constructing moduli spaces of stable Ulrich bundles of arbitrary rank and…

In the high-energy quantum-physics literature one finds statements such as "matrix algebras converge to the sphere". Earlier I provided a general precise setting for understanding such statements, in which the matrix algebras are viewed as…

We discuss some specializations of the frames of flat orthonormal frame bundles over geometries of indefinite signature, and the resulting symmetries of families of embedded Riemannian or pseudo-Riemannian geometries. The specializations…

We present a survey on the moduli spaces of rank 2 quadric bundles over a compact Riemann surface X. These are objects which generalise orthogonal bundles and which naturally occur through the study of the connected components of the moduli…

It has recently been proved that the category of N-manifolds of degree $n$, that is, $\mathbb N$-graded supermanifolds of degree $n$ for which the parity agrees with the gradation, is equivalent to the category of purely even $n$-tuple…

There is a natural filtration on the space of degree-$k$ homogeneous polynomials in $n$ independent variables with coefficients in the algebra of smooth functions on the Grassmannian $\mathrm{Gr}(n,s)$, determined by the tautological…

In this paper, we give a full classification of all homogeneous Ulrich bundles on a Grassmannian $\Gr(k,n)$ of $k$-planes on $\PP^n$.

We investigate the orientability of a class of vector bundles over flag manifolds of real semi-simple Lie groups, which include the tangent bundle and also stable bundles of certain gradient flows. Closed formulas, in terms of roots, are…

This note describes sharp Milnor--Wood inequalities for the Euler number of flat oriented vector bundles over closed Riemannian manifolds locally isometric to products of hyperbolic planes. One consequence is that such manifolds do not…

We classify Ulrich vector bundles that are not big on smooth complex surfaces and threefolds.

One of the most appealing results of metric-affine gauge theory of gravity is a close parallel between the Riemann curvature two-form and the Cartan torsion two-form: While the former is the field strength of the Lorentz-group connection…