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Pointed Blaschke manifolds and geodesic normal sections

Published online by Cambridge University Press:  17 April 2009

Dong-Soo Kim ,
Young Ho Kim  and
Eun Kyoung Lee
Dong-Soo Kim
Affiliation:
Department of Mathematics, Connam National University, K wangju 535–737, Korea e-mail: [email protected]
Young Ho Kim
Affiliation:
Department of Mathematics, Kyungpook National University, Taegu 702–701, Korea e-mail: [email protected]
Eun Kyoung Lee
Affiliation:
Department of Mathematics, Connam National University, K wangju 535–737, Korea e-mail: [email protected]
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We study complete submanifolds of Euclidean space where every geodesic passing through a fixed point is the normal section along it. We prove that all such geodesics are independent of the direction at the point and such submanifolds are pointed Blaschke manifolds or diffeomorphic to a Euclidean space.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 70 , Issue 3 , December 2004 , pp. 377 - 383
Copyright
Copyright © Australian Mathematical Society 2004

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