AI Networking Cookbook: Practical recipes for AI-assisted network automation and development
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We introduce and study a Yamabe-type variational problem associated with the curl operator on middle-degree forms on a closed oriented Riemannian manifold $(M^n,g)$ with $n\equiv3\pmod4$. The corresponding curl--Yamabe constant is defined by minimizing a conformally invariant, gauge-invariant quotient built from $\|{\r...
Let $u:\mathbb{S}^{2n+1}\to\mathbb{CP}^n$ be a smooth nonconstant harmonic map. We prove that its Morse index is equal to $ 2n+2$ if and only if \begin{equation*} u = h \circ \pi \circ \Xi, \end{equation*} where $\Xi:\mathbb{S}^{2n+1}\to\mathbb{S}^{2n+1}$ is an isometric transformation, $\pi:\mathbb{S}^{2n+1}\to\mathbb...
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