Geodesic
A Constraint on Chern Classes of Strictly Pseudoconvex CR Manifolds
Symmetry, integrability and geometry: methods and applications, Tome 16 (2020) Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This short paper gives a constraint on Chern classes of closed strictly pseudoconvex CR manifolds (or equivalently, closed holomorphically fillable contact manifolds) of dimension at least five. We also see that our result is “optimal” through some examples.
Keywords: strictly pseudoconvex CR manifold, holomorphically fillable, Chern class. 
@article{SIGMA_2020_16_a4,
     author = {Yuya Takeuchi},
     title = {A {Constraint} on {Chern} {Classes} of {Strictly} {Pseudoconvex} {CR} {Manifolds}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2020},
     volume = {16},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a4/}
}
TY  - JOUR
AU  - Yuya Takeuchi
TI  - A Constraint on Chern Classes of Strictly Pseudoconvex CR Manifolds
JO  - Symmetry, integrability and geometry: methods and applications
PY  - 2020
VL  - 16
UR  - http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a4/
LA  - en
ID  - SIGMA_2020_16_a4
ER  - 
%0 Journal Article
%A Yuya Takeuchi
%T A Constraint on Chern Classes of Strictly Pseudoconvex CR Manifolds
%J Symmetry, integrability and geometry: methods and applications
%D 2020
%V 16
%U http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a4/
%G en
%F SIGMA_2020_16_a4
Yuya Takeuchi. A Constraint on Chern Classes of Strictly Pseudoconvex CR Manifolds. Symmetry, integrability and geometry: methods and applications, Tome 16 (2020). http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a4/

[1] Boutet de Monvel L., “Intégration des équations de Cauchy–Riemann induites formelles”, Équations aux derivées partielles linéaires et non linéaires, Séminaire Goulaouic–Lions–Schwartz, 1974–1975, no. 9, Centre Math., École Polytech., Paris, 1975, 14 pp. | MR

[2] Bungart L., “Vanishing cup products on pseudoconvex CR manifolds”, The Madison Symposium on Complex Analysis (Madison, WI, 1991), Contemp. Math., 137, Amer. Math. Soc., Providence, RI, 1992, 105–111 | DOI | MR

[3] Cao J., Chang S.-C., “Pseudo-Einstein and $Q$-flat metrics with eigenvalue estimates on CR-hypersurfaces”, Indiana Univ. Math. J., 56 (2007), 2839–2857, arXiv: math.DG/0609312 | DOI | MR | Zbl

[4] Case J. S., Gover A. R., “The $P'$-operator, the $Q'$-curvature, and the CR tractor calculus”, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (to appear) , arXiv: 1709.08057

[5] Etnyre J. B., Ozbagci B., “Invariants of contact structures from open books”, Trans. Amer. Math. Soc., 360 (2008), 3133–3151, arXiv: math.GT/0605441 | DOI | MR | Zbl

[6] Harvey F. R., Lawson H. B. (Jr.), “On boundaries of complex analytic varieties. I”, Ann. of Math., 102 (1975), 223–290 | DOI | MR | Zbl

[7] Kollár J., “Links of complex analytic singularities”, Surveys in Differential Geometry. Geometry and Topology, Surv. Differ. Geom., 18, Int. Press, Somerville, MA, 2013, 157–193, arXiv: 1209.1754 | DOI | MR | Zbl

[8] Lempert L., “Algebraic approximations in analytic geometry”, Invent. Math., 121 (1995), 335–353 | DOI | MR

[9] Marugame T., “Renormalized Chern–Gauss–Bonnet formula for complete Kähler–Einstein metrics”, Amer. J. Math., 138 (2016), 1067–1094, arXiv: 1309.2766 | DOI | MR | Zbl

[10] Ohsawa T., “A reduction theorem for cohomology groups of very strongly $q$-convex Kähler manifolds”, Invent. Math., 63 (1981), 335–354 | DOI | MR | Zbl

[11] Ohsawa T., “Addendum to: "A reduction theorem for cohomology groups of very strongly $q$-convex Kähler manifolds"”, Invent. Math., 66 (1982), 391–393 | DOI | MR | Zbl

[12] Popescu-Pampu P., “On the cohomology rings of holomorphically fillable manifolds”, Singularities II, Contemp. Math., 475, Amer. Math. Soc., Providence, RI, 2008, 169–188, arXiv: 0712.3484 | DOI | MR | Zbl