# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1703.09569