In "The Ricci Flow: An Introduction", the authors define a $\delta$-necklike point of the Ricci flow as a point $(x, t)$ where $$\|\text{Rm} - R (\theta \otimes \theta)\| \leq \delta \|\text{Rm}\|$$ for some unit $2$-form $\theta$. I'm having a bit of trouble understanding how this motivatives the "necklike" nomenclature. Intuitively, the above condition would imply that $\text{Rm} \approx R (\theta \otimes \theta)$, but what does this mean geometrically and how does it justify the "necklike" part of the definition? I thought a reasonable guess would be that this would be in reference to a $\delta$-neck of the form $\mathbb{S}^{n}(\delta) \times I$ (i.e, the geometry of the manifold at $(x, t)$ is arbitrarily close to the geometry of this neck), but I fail to see how the curvature tensor of such a neck can be expressed in the form of $R (\theta \otimes \theta)$. I'd appreciate any help! Thanks in advance

In "The Ricci Flow: An Introduction", the authors define a $\delta$-necklike point of the Ricci flow as a point $(x, t)$ where $$\|\text{Rm} - R (\theta \otimes \theta)\| \leq \delta \|\text{Rm}\|$$ for some unit $2$-form $\theta$. I'm having a bit of trouble understanding how this motivates the "necklike" nomenclature. Intuitively, the above condition would imply that $\text{Rm} \approx R (\theta \otimes \theta)$, but what does this mean geometrically and how does it justify the "necklike" part of the definition? I thought a reasonable guess would be that this would be in reference to a $\delta$-neck of the form $\mathbb{S}^{n}(\delta) \times I$ (i.e, the geometry of the manifold at $(x, t)$ is arbitrarily close to the geometry of this neck), but I fail to see how the curvature tensor of such a neck can be expressed in the form of $R (\theta \otimes \theta)$. I'd appreciate any help! Thanks in advance