Journal of the Korean Mathematical Society (대한수학회지)
- Volume 33 Issue 3
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- Pages.507-512
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- 1996
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- 0304-9914(pISSN)
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- 2234-3008(eISSN)
TOTALLY UMBILIC LORENTZIAN SUBMANIFOLDS
- Ahn, Seong-Soo (Department of Mathematics Dongshin University ) ;
-
Kim, Dong-Soo
(Department of Mathematics Chonnam National University )
;
- Kim, Young-Ho (Department of Mathematics Teachers College Kyungpook National University )
- Published : 1996.08.01
Abstract
A totally umbilic submanifold of a pseudo-Riemanian manifold is a submanifold whose first fundamental form and second fundamental form are proportiona. An ordinary hypersphere $S^n(r)$ of an affine (n + 1)-space of the Euclidean space $E^m$ is the best known example of totally umbilic submanifolds of $E^m$.