A Constraint on Chern Classes of Strictly Pseudoconvex CR Manifolds

TL;DR

This paper establishes a new constraint on the Chern classes of certain high-dimensional CR manifolds, demonstrating the optimality of this constraint with specific examples.

Contribution

It introduces a novel restriction on Chern classes for closed strictly pseudoconvex CR manifolds of dimension five or higher, expanding understanding of their geometric properties.

Findings

Derived a new constraint on Chern classes

Showed the constraint is optimal with examples

Enhanced understanding of CR manifold geometry

Abstract

This short paper gives a constraint on Chern classes of closed strictly pseudoconvex CR manifolds (or equivalently, closed holomorphically fillable contact manifolds) of dimension at least five. We also see that our result is ''optimal'' through some examples.