Complete surfaces with non-positive extrinsic curvature in H3 and S3
نویسندگان
چکیده
منابع مشابه
Complete surfaces with negative extrinsic curvature
N. V. Efimov [Efi64] proved that there is no complete, smooth surface in R with uniformly negative curvature. We extend this to isometric immersions in a 3-manifold with pinched curvature: if M has sectional curvature between two constants K2 and K3, then there exists K1 < min(K2, 0) such that M contains no smooth, complete immersed surface with curvature below K1. Optimal values of K1 are dete...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2015
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2015.05.049