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Positive sectional curvatures does not imply positive Gauss-Bonnet integrand. (English) Zbl 0325.53042


MSC:

53C20 Global Riemannian geometry, including pinching
Full Text: DOI

References:

[1] R. L. Bishop and S. I. Goldberg, Some implications of the generalized Gauss-Bonnet theorem, Trans. Amer. Math. Soc. 112 (1964), 508 – 535. · Zbl 0133.15101
[2] Shiing-shen Chern, On curvature and characteristic classes of a Riemann manifold, Abh. Math. Sem. Univ. Hamburg 20 (1955), 117 – 126. · Zbl 0066.17003 · doi:10.1007/BF02960745
[3] Alfred Gray, The six dimensional Gauss Bonnet integrand, Proc. Amer. Math. Soc. 38 (1973), 374 – 380. · Zbl 0277.53034
[4] Hans Samelson, On curvature and characteristic of homogeneous spaces, Michigan Math. J. 5 (1958), 13 – 18. · Zbl 0084.37407
[5] John A. Thorpe, Some remarks on the Gauss-Bonnet integral, J. Math. Mech. 18 (1969), 779 – 786. · Zbl 0183.50503
[6] Alan Weinstein, Remarks on curvature and the Euler integrand, J. Differential Geometry 6 (1971/72), 259 – 262. · Zbl 0226.53019
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