\( \newcommand{\RR}{\mathbb{R}} \newcommand{\CC}{\mathbb{C}} \newcommand{\SS}{\mathbb{S}} \newcommand{\NN}{\mathbb{N}} \newcommand{\ZZ}{\mathbb{Z}} \newcommand{\Ric}{\operatorname{Ric}} \newcommand{\Tr}{\operatorname{Tr}} \newcommand{\Img}{\operatorname{Img}} \newcommand{\Id}{\operatorname{Id}} \newcommand{\avgint}{\mathop{\mathchoice{\,\rlap{-}\!\!\int}{\rlap{\raise.15em{\scriptstyle -}}\kern-.2em\int}{\rlap{\raise.09em{\scriptscriptstyle -}}\!\int}{\rlap{-}\!\int}}\nolimits} \newcommand{\abs}[1]{\left\lvert{#1}\right\rvert} \newcommand{\ip}[2]{\left\langle{#1},{#2}\right\rangle} \renewcommand{\vec}[1]{\overrightarrow{\mathbf{#1}}} \newcommand{\vecna}[1]{\mathbf{#1}} \DeclareMathOperator{\graph}{Gr} \DeclareMathOperator{\area}{Area} \DeclareMathOperator{\Rm}{Rm} \DeclareMathOperator{\ric}{Ric} \DeclareMathOperator{\arclen}{Len} \DeclareMathOperator{\divg}{div} \DeclareMathOperator{\curl}{curl} \newcommand{\hugezero}{\huge 0} \)