Chern classes of spherical CR manifolds

TL;DR

This paper constructs spherical CR manifolds with non-trivial Chern classes, establishes constraints on these classes, and identifies topological obstructions to certain CR structures, advancing understanding of their geometric and topological properties.

Contribution

It introduces the first examples of spherical CR manifolds with non-trivial Chern classes and provides new constraints and obstructions related to their topology and geometry.

Findings

Constructed closed spherical CR manifolds with non-trivial first Chern class.

Proved constraints on Chern classes of spherical CR manifolds.

Identified topological obstructions to spherical CR structures on contact manifolds.

Abstract

We first construct closed spherical CR manifolds of dimension at least five having non-trivial first Chern class with real coefficients. We next prove a constraint on Chern classes with real coefficients of (not necessarily closed) spherical CR manifolds. Finally, we obtain a topological obstruction to the existence of spherical CR structures on co-oriented contact manifolds.