Related papers: Higher Obstructions of Complex Supermanifolds

The purpose of this paper is to produce restrictions on fundamental groups of manifolds admitting good complexifications by proving the following Cheeger-Gromoll type splitting theorem: Any closed manifold $M$ admitting a good…

We begin with a brief discussion of the building blocks of supersymmetric grand unified theories. We recall some of the compelling theoretical reasons for viewing supersymmetric grand unification as an attractive avenue for physics beyond…

We say that a cover of surfaces S -> X has the Birman--Hilden property if the subgroup of the mapping class group of X consisting of mapping classes that have representatives that lift to S embeds in the mapping class group of S modulo the…

We define the notion of an exceptional manifold to be a flat Riemannian manifold with boundary which supports a positive harmonic function satisfying simultaneously a zero Dirichlet condition and a constant (nonzero) Neumann condtion at the…

We study Brauer-Manin obstructions to integral points on open subsets of the projective plane.

This paper is a review of recent and classical results on integrable geodesic flows on Riemannian manifolds and topological obstructions to integrability. We also discuss some open problems.

We introduce variational obstacle avoidance problems on Riemannian manifolds and derive necessary conditions for the existence of their normal extremals. The problem consists of minimizing an energy functional depending on the velocity and…

A nonstandard (maximal) inclusion SO(3) in SO(5) associated with the irreducible representation \rho_5 of SO(3) in R^5 is considered. The topological obstructions for admitting the SO(3) structure on the frame bundle over 5-manifold are…

A notion of vector field cobordism for oriented manifolds was defined by B\"okstedt and Svane. We extend this notion to define complex section cobordism for almost complex manifolds. We then determine the complex section cobordism groups…

In this article we introduce a variational approach to collision avoidance of multiple agents evolving on a Riemannian manifold and derive necessary conditions for extremals. The problem consists of finding non-intersecting trajectories of…

We find new obstructions to the existence of complete Riemannian metric of nonnegative sectional curvature on manifolds with infinite fundamental groups. In particular, we construct many examples of vector bundles whose total spaces admit…

Strong approximation with Brauer-Manin obstruction is established for smooth varieties containing a connected linear algebraic group with a compatible action.

We review a class of models of dynamical supersymmetry breaking, and give a unified description of these models.

We classify the admissible types of constraint (hermitian, holomorphic, with reality conditions on the bosonic sectors, etc.) for generalized supersymmetries in the presence of complex spinors. We further point out which constrained…

In this paper, we mainly focus on formal deformation theory of module homomorphisms. We first introduce the cohomology of module homomorphisms and study formal one-parameter deformation. We obtain some properties about obstructions. Then we…

We provide integral curvature bounds for compact Riemannian manifolds that allow isometric immersions into a Euclidean space with low codimension in terms of the Betti numbers.

The aim of this paper is to describe a large class of Hermitian Gray manifolds.

We introduce new obstructions to rationality for geometrically rational threefolds arising from the geometry of curves and their cycle maps.

We prove necessary and sufficient conditions for a smooth surface in a 4-manifold X to be pseudoholomorphic with respect to some almost complex structure on X. This provides a systematic approach to the construction of pseudoholomorphic…

Submanifold theory is a very active vast research field which plays an important role in the development of modern differential geometry. This branch of differential geometry is still so far from being exhausted; only a small portion of an…