Artículos de revistas
Riemannian Submersions Of Open Manifolds Which Are Flat At Infinity
Registro en:
Anais Da Academia Brasileira De Ciencias. , v. 70, n. 1, p. 7 - 14, 1998.
13765
2-s2.0-0346334475
Autor
Marenich V.
Institución
Resumen
We prove that a base Bn-k of a Riemannian submersion π : Mn → Bn-k is flat, if Mn is flat at infinity and Bn-k is compact. As a corollary we obtain a topological gap-phenomenon for open manifolds of nonnegative sectional curvature. 70 1 7 14 Cheeger, J., Gromoll, D., On the structure of complete manifolds of nonnegative curvature (1972) Ann. Math., 96 (3), pp. 413-443 Eschenburg, J.-H., Schroeder, V., Strake, M., Curvature at infinity of open nonnegatively curved manifolds (1989) J. Diff. Geom., 30, pp. 155-166 Gromoll, D., Grove, K., The low-dimensional metric foliations of euclidean spheres (1988) J. Diff. Geom., 28, pp. 143-156 Kasue, A., Sugahara, K., Gap theorems for certain submanifolds of euclidean spaces and hyperbolic space forms (1987) Osaka J. Math., 24, pp. 679-704 Marenich, V., The topological gap phenomenon for open manifolds of nonnegative curvature (1985) Soviet Math. Dokl., 32, pp. 440-443 Marenich, V., The metric structure of open manifolds of nonnegative curvature (1981) Soviet Math. Dokl., 24, pp. 595-597. , complete version (in russian) under the same title in: Ukraine Geom. Sb., no. 26 (1983), 79-96 Marenich, V., The holonomy in open manifolds of nonnegative curvature (1996) Mich. Math. J., 43 (2), pp. 263-272 O'Neil, B., The fundamental equations of submersion (1966) Mich. Math. J., 13 (4), pp. 459-469 O'Neil, B., Submersions and geodesics (1967) Duke Math. J., 34, pp. 363-373 Perelman, G., Proof of the soul conjecture of Cheeger and Gromoll (1994) J. Diff. Geom., 40, pp. 209-212 Walschap, G., Metric foliations and curvature (1992) J. Geom. Anal., 2, pp. 373-381