Isotropic curvature: A survey

Harish Seshadri[1]

  • [1] Indian Institute of Science Department of mathematics Bangalore 560012 (India)

Séminaire de théorie spectrale et géométrie (2007-2008)

  • Volume: 26, page 139-144
  • ISSN: 1624-5458

Abstract

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We discuss the notion of isotropic curvature of a Riemannian manifold and relations between the sign of this curvature and the geometry and topology of the manifold.

How to cite

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Seshadri, Harish. "Isotropic curvature: A survey." Séminaire de théorie spectrale et géométrie 26 (2007-2008): 139-144. <http://eudml.org/doc/11234>.

@article{Seshadri2007-2008,
abstract = {We discuss the notion of isotropic curvature of a Riemannian manifold and relations between the sign of this curvature and the geometry and topology of the manifold.},
affiliation = {Indian Institute of Science Department of mathematics Bangalore 560012 (India)},
author = {Seshadri, Harish},
journal = {Séminaire de théorie spectrale et géométrie},
keywords = {Weyl Curvature; Euler Characteristic; Chern-Gauss-Bonnet Theorem; Asymptotically Flat Manifolds; Yamabe metric; Weyl curvature; Euler characteristic; Chern-Gauss-Bonnet theorem; asymptotically flat manifolds},
language = {eng},
pages = {139-144},
publisher = {Institut Fourier},
title = {Isotropic curvature: A survey},
url = {http://eudml.org/doc/11234},
volume = {26},
year = {2007-2008},
}

TY - JOUR
AU - Seshadri, Harish
TI - Isotropic curvature: A survey
JO - Séminaire de théorie spectrale et géométrie
PY - 2007-2008
PB - Institut Fourier
VL - 26
SP - 139
EP - 144
AB - We discuss the notion of isotropic curvature of a Riemannian manifold and relations between the sign of this curvature and the geometry and topology of the manifold.
LA - eng
KW - Weyl Curvature; Euler Characteristic; Chern-Gauss-Bonnet Theorem; Asymptotically Flat Manifolds; Yamabe metric; Weyl curvature; Euler characteristic; Chern-Gauss-Bonnet theorem; asymptotically flat manifolds
UR - http://eudml.org/doc/11234
ER -

References

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  1. S. Brendle Einstein manifolds with nonnegative isotropic curvature are locally symmetric, arXiv:0812.0335 Zbl1189.53042
  2. S. Brendle, R. Schoen, Manifolds with 1/4-pinched Curvature are Space Forms, To appear in the Journal of American Mathematical Society. Zbl1251.53021MR2449060
  3. S. Brendle, R. Schoen, Classification of manifolds with weakly 1/4-pinched curvatures, Acta Mathematica 200 (2008), 1-13. Zbl1157.53020MR2386107
  4. A. Fraser, Fundamental groups of manifolds with positive isotropic curvature, Ann. of Math. (2) 158 (2003), no. 1, 345-354. Zbl1044.53023MR1999925
  5. A. Fraser, The fundamental group of manifolds of positive isotropic curvature and surface groups, Duke Math. J. 133 (2006), no. 2, 325-334. Zbl1110.53027MR2225695
  6. S. Gadgil, H. Seshadri On the topology of manifolds with positive isotropic curvature, Proc. Amer. Math. Soc. 137 (2009), 1807-1811. Zbl1166.53026MR2470841
  7. M. Gromov, Asymptotic invariants of infinite groups, Geometric group theory, Vol. 2 (Sussex, 1991), 1-295, London Math. Soc. Lecture Note Ser., 182, Cambridge Univ. Press, Cambridge, 1993 Zbl0841.20039MR1253544
  8. R. S. Hamilton, Four-manifolds with positive isotropic curvature, Comm. Anal. Geom. 5 (1997), no. 1, 1-92. Zbl0892.53018MR1456308
  9. M. Micallef, J. 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. Zbl0661.53027MR924677
  10. M. Micallef, M. Wang, Metrics with nonnegative isotropic curvature, Duke Math. J. 72 (1993), no. 3, 649-672. Zbl0804.53058MR1253619
  11. R. Schoen, http://www.math.washington.edu/~lee/PNGS/2007-fall/schoen-problems.pdf 
  12. W. Seaman, On manifolds with nonnegative curvature on totally isotropic 2-planes, Trans. Amer. Math. Soc. 338 (1993), no. 2, 843-855. Zbl0785.53034MR1123458
  13. H. Seshadri, A note on negative isotropic curvature, Math. Res. Lett. 11 (2004), no. 2-3, 365-370. Zbl1073.53050MR2067480
  14. H. Seshadri, Manifolds with nonnegative isotropic curvature, http://www.math.iisc.ernet.in/~harish/papers/pic-cag.pdf Zbl1197.53047

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