By Bartell F.E.
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One sunny day on his postal course, Vincent Wyckoff crosses the trail of an aged gentleman whistling for his misplaced parakeet. The previous guy is disillusioned, and Wyckoff strikes down the block slowly, having a look low and high, hoping to identify the little poultry. He reaches the man’s apartment and gives sympathy to his spouse, who smiles unfortunately and says, “We haven’t had that poultry for twenty-five years.
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Extra resources for Anomalous Osmose (1920)(en)(5s)
Case (a) above, with A = 0, corresponds to |C| = |D|, and in this case N is a subset of an afﬁne special Lagrangian 3-plane R3 in C3 . If |C| = |D| then N is an embedded submanifold diffeomorphic to R3 , with coordinates (x1 , x2 , t). The two cases C = 0 and D = 0 are constructed by [7, Prop. 3] with n = 2, m = 3 and G = R, as in [7, Ex. 6] and case (c) above, with the symmetry group G of N acting by (x1 , x2 , t) → (x1 , x2 , t + c). Constructing special Lagrangian m-folds in Cm 797 Acknowledgements.
R. B. Lawson, Calibrated geometries, Acta Math. 148 (1982), 47–157 6. D. Joyce, On counting special Lagrangian homology 3-spheres, hep-th/9907013, 1999 7. D. DG/0008021, 2000 8. D. DG/0010036, 2000 9. D. DG/0011179, 2000 10. D. DG/0012060, 2000 11. D. DG/0101249, 2001 12. G. Lawlor, The angle criterion, Inventiones math. 95 (1989), 437–446 13. A. -T. Yau, E. Zaslow, Mirror symmetry is T-duality, Nucl. Phys. B479 (1996), 243–259.
Let us parametrize the circle C+ with a parameter s, so that C+ = x1 (s), x2 (s), x3 (s) : s ∈ R . This gives a parametrization Φ : R2 → Σ+ of Σ+ , by Φ : (s, t) → w1 (t)x1 (s), w2 (t)x2 (s), w3 (t)x3 (s) . 4) We shall calculate the conditions upon xj (s) for Φ to be conformal, and solve them. Since the xj (s) satisfy α1 x12 + α2 x22 + α3 x32 = 1 and x12 − x22 − x32 = 0, differentiating with respect to s gives α1 x1 x˙1 + α2 x2 x˙2 + α3 x3 x˙3 = 0 and x1 x˙1 − x2 x˙2 − x3 x˙3 = 0, where ‘ ˙ ’is dsd .