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- W4386554969 abstract "Given a calibration $alpha$ whose stabilizer acts transitively on the Grassmanian of calibrated planes, we introduce a nontrivial Lie-theoretic condition on $alpha$, which we call compliancy, and show that this condition holds for many interesting geometric calibrations, including Kahler, special Lagrangian, associative, coassociative, and Cayley. We determine a sufficient condition that ensures compliancy of $alpha$, we completely characterize compliancy in terms of properties of a natural involution determined by a calibrated plane, and we relate compliancy to the geometry of the calibrated Grassmanian. The condition that a Riemannian immersion $iota colon L to M$ be calibrated is a first order condition. By contrast, its extrinsic geometry, given by the second fundamental form $A$ and the induced tangent and normal connections $nabla$ on $TL$ and $D$ on $NL$, respectively, is second order information. We characterize the conditions imposed on the extrinsic geometric data $(A, nabla, D)$ when the Riemannian immersion $iota colon L to M$ is calibrated with respect to a calibration $alpha$ on $M$ which is both parallel and compliant. This motivate the definition of an infinitesimally calibrated Riemannian immersion, generalizing the classical notion of a superminimal surface in $mathbb R^4$." @default.
- W4386554969 created "2023-09-09" @default.
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- W4386554969 date "2023-09-06" @default.
- W4386554969 modified "2023-10-18" @default.
- W4386554969 title "Extrinsic geometry of calibrated submanifolds" @default.
- W4386554969 doi "https://doi.org/10.48550/arxiv.2309.03428" @default.
- W4386554969 hasPublicationYear "2023" @default.
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