Geometric Theory of Weyl Structures

References

[1] U. Bader, C. Frances, K. Melnick, An embedding theorem for automorphism groups of Cartan geometries, Geom. Funct. Anal. 19 (2009), 333–355. MR

[2] T. N. Bailey, M. G. Eastwood, A. R. Gover, Thomas’s structure bundle for conformal, projective and related structures, Rocky Mountain J. Math. 24 (1994), 1191–1217. MR

[3] R. J. Baston, Almost Hermitian symmetric manifolds. I. Local twistor theory, Duke Math. J. 63 (1991), 81–112. MR

[4] R. J. Baston, Almost Hermitian symmetric manifolds. II. Differential invariants, Duke Math. J. 63 (1991), 113–138. MR

[5] T. Branson, A. Čap, M. Eastwood, A. R. Gover, Prolongations of geometric overdetermined systems, Internat. J. Math. 17 (2006), 641–664. MR

[6] R. L. Bryant, Bochner-Kähler metrics, J. Amer. Math. Soc. 14 (2001), 623–715. MR

[7] E. Calabi, Complete affine hyperspheres. I, Symposia Mathematica, Vol. X (Convegno di Geometria Differenziale, INDAM, Rome, 1971), (1972), 19–38. MR zbM

[8] D. M. J. Calderbank, Selfdual 4-manifolds, projective surfaces, and the Dunajski-West construction, SIGMA Symmetry Integrability Geom. Methods Appl. 10 (2014), Paper 035, 18. MR zbM

[9] D. M. J. Calderbank, T. Diemer, Differential invariants and curved Bernstein-Gelfand-Gelfand sequences, J. Reine Angew. Math. 537 (2001), 67–103. MR

[10] D. M. J. Calderbank, T. Diemer, V. Souček, Ricci-corrected derivatives and invariant differential operators, Differential Geom. Appl. 23 (2005), 149–175. MR

[11] A. Čap, A. R. Gover, M. Hammerl, Holonomy reductions of Cartan geometries and curved orbit decompositions, Duke Math. J. 163 (2014), 1035–1070. MR

[12] A. Čap, A. R. Gover, H. R. Macbeth, Einstein metrics in projective geometry, Geom. Dedicata 168 (2014), 235–244. MR

[13] A. Čap, A. R. Gover, Projective compactifications and Einstein metrics, J. Reine Angew. Math. 717 (2016), 47–75. MR

[14] A. Čap, J. Slovák, V. Souček, Invariant operators on manifolds with almost Hermitian symmetric structures. I. Invariant differentiation, Acta Math. Univ. Comenian. (N.S.) 66 (1997), 33–69. MR

[15] A. Čap, J. Slovák, Weyl structures for parabolic geometries, Math. Scand. 93 (2003), 53–90. MR

[16] A. Čap, J. Slovák, Parabolic geometries I, Mathematical Surveys and Monographs 154, American Mathematical Society, Providence, RI, 2009, Background and general theory. MR

[17] A. Čap, J. Slovák, V. Souček, Bernstein-Gelfand-Gelfand sequences, Ann. of Math. 154 (2001), 97–113. MR

[18] M. Chursin, L. Schäfer, K. Smoczyk, Mean curvature flow of space-like Lagrangian submanifolds in almost para-Kähler manifolds, Calc. Var. Partial Differential Equations 41 (2011), 111–125. MR

[19] M. Dunajski, T. Mettler, Gauge theory on projective surfaces and anti-self-dual Einstein metrics in dimension four, J. Geom. Anal. 28 (2018), 2780–2811. MR

[20] C. Frances, Sur le groupe d’automorphismes des géométries paraboliques de rang 1, Ann. Sci. École Norm. Sup. (4) 40 (2007), 741–764. MR

[21] M. Herzlich, Parabolic geodesics as parallel curves in parabolic geometries, Internat. J. Math. 24 (2013), 1350067, 16. MR

[22] R. Hildebrand, The cross-ratio manifold: a model of centro-affine geometry, Int. Electron. J. Geom. 4 (2011), 32–62. MR zbM

[23] R. Hildebrand, Half-dimensional immersions in para-Kähler manifolds, Int. Electron. J. Geom. 4 (2011), 85–113. MR zbM

[24] S. Kobayashi, T. Nagano, On filtered lie algebras and geometric structures. I, J. Math. Mech. 13 (1964), 875–907. MR

[25] F. Labourie, Flat projective structures on surfaces and cubic holomorphic differentials, Pure Appl. Math. Q. 3 (2007), 1057–1099. MR zbM

[26] J. C. Loftin, Affine spheres and convex \(\mathbb{RP}^n\)-manifolds, Amer. J. Math. 123 (2001), 255–274. MR zbM

[27] T. Mettler, Geodesic rigidity of conformal connections on surfaces, Math. Z. 281 (2015), 379–393. MR

[28] T. Mettler, Minimal Lagrangian connections on compact surfaces, Adv. Math. 354 (2019). MR zbM

[29] T. Mettler, Extremal conformal structures on projective surfaces, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) XX (2020), 1621–1663.

[30] T. Mettler, G. P. Paternain, Convex projective surfaces with compatible Weyl connection are hyperbolic, 2018, to appear in Anal. PDE. arXiv:1804.04616

[31] T. Mettler, G. P. Paternain, Holomorphic differentials, thermostats and Anosov flows, Math. Ann. 373 (2019), 553–580. MR zbM

[32] A. Wienhard, An invitation to higher Teichmüller theory, 2018. arXiv:1803.06870