no. 13-14
Differential Geometry
Complete intersections with metrics of positive scalar curvature

Presented by: Jean-Michel Bismut

Fang, Fuquan1; Shao, Peng2
1 Department of Mathematics, Capital Normal University, Beijing, PR China
2 Chern Institute of Mathematics, Nankai University, Weijin Road 94, Tianjin 300071, PR China
Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 797-800.

We give a complete list of complex projective complete intersections admitting Riemannian metrics of positive scalar curvature.

Nous donnons la liste des variétés complexes projectives intersections complètes, qui admettent une métrique riemannienne à courbure scalaire positive.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.03.033
Fang, Fuquan 1; Shao, Peng 2

1 Department of Mathematics, Capital Normal University, Beijing, PR China
2 Chern Institute of Mathematics, Nankai University, Weijin Road 94, Tianjin 300071, PR China 
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Fang, Fuquan; Shao, Peng. Complete intersections with metrics of positive scalar curvature. Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 797-800. doi : 10.1016/j.crma.2009.03.033. http://www.numdam.org/articles/10.1016/j.crma.2009.03.033/

[1] Barth, W.; Peters, C.; Van de Ven, A. Compact Complex Surfaces, Springer-Verlag, Berlin, 1984

[2] Brooks, R. The Aˆ-genus of complex hypersurfaces and complete intersections, Proc. Amer. Math. Soc., Volume 87 (1983), pp. 528-532

[3] Feng, H.; Zhang, B. Existence of Riemannian metrics with positive scalar curvature of complex complete intersections, Adv. Math. (China), Volume 36 (2007), pp. 47-50

[4] Gromov, M.; Lawson, B. Spin and scalar curvature in the presence of a fundamental group. I, Ann. Math., Volume 111 (1980), pp. 209-230

[5] Gromov, M.; Lawson, B. The classification of simply connected manifolds of positive scalar curvature, Ann. Math., Volume 111 (1980), pp. 423-434

[6] Gromov, M.; Lawson, B. Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Inst. Hautes Études Sci. Publ. Math., Volume 58 (1983), pp. 83-196

[7] Miyaoka, Y. On the Chern numbers of surfaces of general type, Invent. Math., Volume 42 (1977), pp. 225-237

[8] Morgan, J. The Seiberg–Witten Equations and Applications to the Topology of Smooth Four-Manifolds, Princeton Press, 1996

[9] Schoen, R.; Yau, S.T. The structure of manifolds with positive scalar curvature, Manuscripta Math., Volume 28 (1979), pp. 159-183

[10] Stolz, S. Simply connected manifolds of positive scalar curvature, Ann. Math., Volume 136 (1992), pp. 511-540

[11] Taubes, C. The Seiberg–Witten invariants and symplectic forms, Math. Res. Lett., Volume 1 (1994) no. 6, pp. 809-822

[12] Zhang, W. Spinc-manifolds and Rokhlin congruences, C. R. Acad. Sci. Paris, Sér. I Math., Volume 317 (1993), pp. 689-692

[13] Zhang, W. Existence of Riemannian metrics with positive scalar curvature on complex hypersurfaces, Acta Math. Sinica (Chin. Ser.), Volume 39 (1996) no. 4, pp. 460-462

Cited by Sources:

☆ Supported by NSF Grant of China #10671097 and the Capital Normal University.