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Greene, R. E.; Wu, H.

Gap theorems for noncompact Riemannian manifolds. (English) Zbl 0513.53045

Duke Math. J. 49, 731-756 (1982).
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Cited in 6 Reviews
Cited in 36 Documents

MSC:

53C20 Global Riemannian geometry, including pinching

Keywords:

gap theorems; isometric to Rn; pole; simply connected at infinity; sectional curvature

Citations:

Zbl 0487.53034
Cite Review PDF
Full Text: DOI

References:

[1] C. B. Allendoerfer and A. Weil, The Gauss-Bonnet theorem for Riemannian polyhedra , Trans. Amer. Math. Soc. 53 (1943), 101-129. JSTOR: · Zbl 0060.38102 · doi:10.2307/1990134
[2] R. L. Bishop and R. J. Crittenden, Geometry of manifolds , Pure and Applied Mathematics, Vol. XV, Academic Press, New York, 1964. · Zbl 0132.16003
[3] R. Bott and J. Milnor, On the parallelizability of the spheres , Bull. Amer. Math. Soc. 64 (1958), 87-89. · Zbl 0082.16602 · doi:10.1090/S0002-9904-1958-10166-4
[4] J. Cheeger and D. Gromoll, On the structure of complete manifolds of nonnegative curvature , Ann. of Math. (2) 96 (1972), 413-443. JSTOR: · Zbl 0246.53049 · doi:10.2307/1970819
[5] D. Elerath, Open nonnegatively curved \(3\)-manifolds with a point of positive curvature , Proc. Amer. Math. Soc. 75 (1979), no. 1, 92-94. · Zbl 0409.53033 · doi:10.2307/2042679
[6] R. E. Greene and H. Wu, Curvature and complex analysis. II , Bull. Amer. Math. Soc. 78 (1972), 866-870. · Zbl 0258.32003 · doi:10.1090/S0002-9904-1972-13064-7
[7] R. E. Greene and H. Wu, On the subharmonicity and plurisubharmonicity of geodesically convex functions , Indiana Univ. Math. J. 22 (1972/73), 641-653. · Zbl 0235.53039 · doi:10.1512/iumj.1973.22.22052
[8] R. E. Greene and H. Wu, Analysis on noncompact Kähler manifolds , Several complex variables (Proc. Sympos. Pure Math., Vol. XXX, Part 2, Williams Coll., Williamstown, Mass., 1975), Amer. Math. Soc., Providence, R.I., 1977, pp. 69-100. · Zbl 0383.32005
[9] R. E. Greene and H. Wu, Function theory on manifolds which possess a pole , Lecture Notes in Mathematics, vol. 699, Springer, Berlin, 1979. · Zbl 0414.53043
[10] R. E. Greene and H. Wu, On a new gap-phenomenon in Riemannian geometry , Amer. Math. Soc. 2 (June, 1981), 410, Abstracts. JSTOR: · Zbl 0487.53034 · doi:10.1073/pnas.79.2.714
[11] R. E. Greene and H. Wu, On a new gap phenomenon in Riemannian geometry , Proc. Nat. Acad. Sci. U.S.A. 79 (1982), no. 2, 714-715. JSTOR: · Zbl 0487.53034 · doi:10.1073/pnas.79.2.714
[12] D. Gromoll and W. Meyer, On complete open manifolds of positive curvature , Ann. of Math. (2) 90 (1969), 75-90. JSTOR: · Zbl 0191.19904 · doi:10.2307/1970682
[13] Th. Hasanis and D. Koutroufiotis, Flatness of Riemannian metrics outside compact sets , (preprint). · Zbl 0538.53048 · doi:10.1512/iumj.1983.32.32009
[14] M. Kervaire, Non-parallelizability of the \(n\)-sphere for \(n>7\) , Proc. Nat. Acad. Sci. 44 (1958), 280-283. · Zbl 0093.37303 · doi:10.1073/pnas.44.3.280
[15] S. Kobayashi and K. Nomizu, Foundations of differential geometry. Vol. II , Interscience Tracts in Pure and Applied Mathematics, No. 15 Vol. II, Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1969. · Zbl 0175.48504
[16] N. Mok, Y.-T. Siu, and S.-T. Yau, The Poincaré-Lelong equation on complete Kähler manifolds , Compositio Math. 44 (1981), no. 1-3, 183-218. · Zbl 0531.32007
[17] R. Sacksteder, On hypersurfaces with no negative sectional curvatures , Amer. J. Math. 82 (1960), 609-630. JSTOR: · Zbl 0194.22701 · doi:10.2307/2372973
[18] Y.-T. Siu and S.-T. Yau, Complete Kähler manifolds with nonpositive curvature of faster than quadratic decay , Ann. of Math. (2) 105 (1977), no. 2, 225-264. JSTOR: · Zbl 0358.32006 · doi:10.2307/1970998
[19] F. W. Warner, Extensions of the Rauch comparison theorem to submanifolds , Trans. Amer. Math. Soc. 122 (1966), 341-356. · Zbl 0139.15601 · doi:10.2307/1994552
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