Conformal Killing $L^{2}-$forms on complete Riemannian manifolds with nonpositive curvature operator

TL;DR

This paper classifies complete Riemannian manifolds with nonpositive curvature operator that admit nonzero conformal Killing L^2-forms and establishes vanishing theorems for such forms under certain conditions.

Contribution

It provides a classification of manifolds with specific geometric structures and proves new vanishing theorems for conformal Killing L^2-forms.

Findings

Classification of manifolds admitting nonzero conformal Killing L^2-forms

Vanishing theorems for conformal Killing L^2-forms on certain manifolds

Results applicable to manifolds with nonpositive curvature operator

Abstract

We give a classification for connected complete locally irreducible Riemannian manifolds with nonpositive curvature operator, which admit a nonzero closed or co-closed conformal Killing $L^{2}-$form. Moreover, we prove vanishing theorems for closed and co-closed conformal Killing $L^{2}-$forms on some complete Riemannian manifolds.