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RIEMANNIAN SUBMANIFOLDS IN LORENTZIAN MANIFOLDS WITH THE SAME CONSTANT CURVATURES
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 Title & Authors
RIEMANNIAN SUBMANIFOLDS IN LORENTZIAN MANIFOLDS WITH THE SAME CONSTANT CURVATURES
Park, Joon-Sang;
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 Abstract
We study nondegenerate immersions of Riemannian manifolds of constant sectional curvatures into Lorentzian manifolds of the same constant sectional curvatures with flat normal bundles. We also give a method to produce such immersions using the so-called Grassmannian system. .
 Keywords
isometric immersion;Lorentzian manifold;constant sectional curvature;flat connection;nondegenerate;Grassmannian system;
 Language
English
 Cited by
 References
1.
M. Bruck, X. Du, J. Park, and C. L. Terng, The submanifold geometry of real Grassmannian systems, Mem. Amer. Math. Soc. 155 (2002), No. 735.

2.
E. Cartan, Sur les variètès de courbure constante d'un espace euclidien ou noneuclidien, Bull. Soc. Math. France 47 (1920), 125-160.

3.
D. Hilbert, Über Flächen von konstanter Gausscher Kriümmung, Trans. Amer. Math. Soc. 2 (1901), 89-99. crossref(new window)

4.
B. O'Neill, Semi-Riemannian Geometry, Academic Press, 1983.

5.
R. Palais and C. L. Terng, Critical Point Theory and Submanifold Geometry, Springer-Verag, LNM 1353, 1988.

6.
K. Tenenblat, Bäcklund's theorem for submanifolds of space forms and a generalized wave equation, Boll. Soc. Brasil. Mat. 16 (1985), 67-92.

7.
K. Tenenblat and C. L. Terng, Bäcklund's theorem for n-dimensional submanifolds of $R^{2n-1}$, Ann. Math. 111 (1980),477-490. crossref(new window)

8.
C. L. Terng, A higher dimensional generalization of the sine-Gordon equation and its soliton theory, Ann. Math. 111 (1980), 491-510. crossref(new window)

9.
C. L. Terng, Soliton equations and differential geometry, Jour. Diff. Geom. 45 (1997), 407-445.