CR and Holomorphic Embeddings and Pseudo-conformally Flat Metrics

TL;DR

This paper investigates the non-embeddability of certain real hypersurfaces into spheres and explores rigidity of conformal maps between Kähler manifolds with pseudo-conformally flat metrics, using curvature properties.

Contribution

It introduces new results on non-embeddability and rigidity for specific classes of hypersurfaces and Kähler manifolds, linking geometric properties to curvature conditions.

Findings

Non-embeddability of real hypersurfaces of involution type into spheres in low codimension

Rigidity results for conformal maps between pseudo-conformally flat Kähler manifolds

Curvature conditions influence embeddability and conformal map rigidity

Abstract

We study the non-embddability property for a class of real hypersurfaces, called real hypersurfaces of involution type, into the sphere in the low codimensional case, by making use of property of a naturally related Gauss curvature. We also study rigidity problems for conformal maps between a class of K\"ahler manifolds with pseud-conformally flat metrics.