Mathematics – Differential Geometry
Scientific paper
2010-01-08
J. Math. Soc. Japan, vol.64, no.1 (2012), pp. 185-200
Mathematics
Differential Geometry
This version 3 is a version to appear in J. Math. Soc. Japan. 13 pages, no figures
Scientific paper
10.2969/jmsj/06410185
Dedicated to Professor K. Shiohama on the occasion of his seventieth birthday: This article is the third in a series of our investigation on a complete non-compact connected Riemannian manifold $M$. In the first series [arXiv:0901.4010], we showed that all Busemann functions on an $M$ which is not less curved than a von Mangoldt surface of revolution are exhaustions, if the total curvature of the surface is greater than $\pi$. A von Mangoldt surface of revolution is, by definition, a complete surface of revolution homeomorphic to Euclidean plane whose Gaussian curvature is non-increasing along each meridian. Our purpose of this series is to generalize the main theorem in [arXiv:0901.4010] to an $M$ which is not less curved than a more general surface of revolution.
Kondo Kei
Tanaka Minoru
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