Witten deformation and divergence-free symmetric Killing 2-tensors

TL;DR

This paper employs Witten deformation techniques with Morse functions to bound and explicitly compute the dimension of divergence-free symmetric Killing 2-tensors on closed Riemannian manifolds, advancing understanding of their geometric properties.

Contribution

It introduces a novel application of Witten deformation to estimate and explicitly determine the dimension of divergence-free symmetric Killing tensors, especially for p=2.

Findings

Upper bound for the dimension of divergence-free symmetric Killing p-tensors.

Explicit calculation of the dimension for p=2.

Application of Morse functions in tensor analysis.

Abstract

Using a Morse function and a Witten deformation argument, we obtain an upper bound for the dimension of the space of divergence-free symmetric Killing $p$-tensors on a closed Riemannian manifold, and calculate it explicitly for $p=2$.