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- W4385211316 abstract "Abstract Let M be an oriented three-dimensional Riemannian manifold. We define a notion of vorticity of local sections of the bundle <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mrow> <m:mi>SO</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>M</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> <m:mo>→</m:mo> <m:mi>M</m:mi> </m:mrow> </m:math> {mathrm{SO}(M)rightarrow M} of all its positively oriented orthonormal tangent frames. When M is a space form, we relate the concept to a suitable invariant split pseudo-Riemannian metric on <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mrow> <m:msub> <m:mi>Iso</m:mi> <m:mi>o</m:mi> </m:msub> <m:mo></m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>M</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> <m:mo>≅</m:mo> <m:mrow> <m:mi>SO</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>M</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:mrow> </m:math> {mathrm{Iso}_{o}(M)congmathrm{SO}(M)} : A local section has positive vorticity if and only if it determines a space-like submanifold. In the Euclidean case we find explicit homologically volume maximizing sections using a split special Lagrangian calibration. We introduce the concept of optimal frame vorticity and give an optimal screwed global section for the three-sphere. We prove that it is also homologically volume maximizing (now using a common one-point split calibration). Besides, we show that no optimal section can exist in the Euclidean and hyperbolic cases." @default.
- W4385211316 created "2023-07-25" @default.
- W4385211316 creator A5011944385 @default.
- W4385211316 date "2023-07-25" @default.
- W4385211316 modified "2023-10-03" @default.
- W4385211316 title "A split special Lagrangian calibration associated with frame vorticity" @default.
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- W4385211316 doi "https://doi.org/10.1515/acv-2022-0036" @default.
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