On compact manifolds with positive isotropic curvature

Labbi, M.-L.

doi:10.1090/S0002-9939-99-05153-9

On compact manifolds with positive isotropic curvature
HTML articles powered by AMS MathViewer

by M.-L. Labbi

Proc. Amer. Math. Soc. 128 (2000), 1467-1474

DOI: https://doi.org/10.1090/S0002-9939-99-05153-9

Published electronically: August 3, 1999

PDF | Request permission

Abstract:

In this paper we construct new Riemannian metrics with positive isotropic curvature on compact manifolds which fiber over the circle. We also study the relationship between the positivity of the isotropic curvature and the positivity of the $p$-curvature.

References

Arthur L. Besse, Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 10, Springer-Verlag, Berlin, 1987. MR 867684, DOI 10.1007/978-3-540-74311-8
Gromov M., Positive curvature, macroscopic dimension, spectral gaps and higher signatures, Preprint I.H.E.S.
Mohammed Labbi, Sur les nombres de Betti des variétés conformément plates, C. R. Acad. Sci. Paris Sér. I Math. 319 (1994), no. 1, 77–80 (French, with English and French summaries). MR 1285902
Labbi M. L., Actions des groupes de Lie presques simples et positivité de la $p$-courbure, Annales de la faculte des sciences de Toulouse, vol5. n2. (1997) 263-276. (France).
Mohammed-Larbi Labbi, Stability of the $p$-curvature positivity under surgeries and manifolds with positive Einstein tensor, Ann. Global Anal. Geom. 15 (1997), no. 4, 299–312. MR 1472322, DOI 10.1023/A:1006553611999
H. Blaine Lawson Jr. and Shing Tung Yau, Scalar curvature, non-abelian group actions, and the degree of symmetry of exotic spheres, Comment. Math. Helv. 49 (1974), 232–244. MR 358841, DOI 10.1007/BF02566731
Mario J. Micallef and John Douglas Moore, Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two-planes, Ann. of Math. (2) 127 (1988), no. 1, 199–227. MR 924677, DOI 10.2307/1971420
Mario J. Micallef and McKenzie Y. Wang, Metrics with nonnegative isotropic curvature, Duke Math. J. 72 (1993), no. 3, 649–672. MR 1253619, DOI 10.1215/S0012-7094-93-07224-9
Mario J. Micallef and Jon G. Wolfson, The second variation of area of minimal surfaces in four-manifolds, Math. Ann. 295 (1993), no. 2, 245–267. MR 1202392, DOI 10.1007/BF01444887
Shin Nayatani, Kleinian groups and conformally flat metrics, Geometry and global analysis (Sendai, 1993) Tohoku Univ., Sendai, 1993, pp. 341–349. MR 1361199
Walter Seaman, On manifolds with nonnegative curvature on totally isotropic 2-planes, Trans. Amer. Math. Soc. 338 (1993), no. 2, 843–855. MR 1123458, DOI 10.1090/S0002-9947-1993-1123458-2