Homology of contact CR-submanifolds

TL;DR

This paper investigates the homology properties of contact CR-submanifolds within real hypersurfaces in complex Euclidean spaces, establishing vanishing theorems and nonexistence results for stable integral currents.

Contribution

It provides new vanishing theorems for homology groups of contact CR-submanifolds in complex space forms, highlighting their topological constraints.

Findings

Nonexistence of stable integral currents on certain submanifolds

Vanishing theorems for homology groups of contact CR-submanifolds

Topological restrictions derived from homology analysis

Abstract

In this paper, homology of a contact CR-submanifold of a real hypersurface, which has naturally almost contact metric structure induced from the complex Euclidean space $\mathbb{C}^{m}$, is examined. More precisely, nonexistence of stable integral currents on a compact contact CR-submanifold of real hypersurface of canonical complex space form $\mathbb{C}^m$ is investigated and vanishing theorems concerning the homology groups are obtained.