A characterization of complete Riemannian manifolds minimally immersed in the unit sphere
1993 ◽
Vol 131
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pp. 127-133
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Keyword(s):
Let Mn be an n-dimensional Riemannian manifold minimally immersed in the unit sphere Sn+p (1) of dimension n + p. When Mn is compact, Chern, do Carmo and Kobayashi [1] proved that if the square ‖h‖2 of length of the second fundamental form h in Mn is not more than , then either Mn is totallygeodesic, or Mn is the Veronese surface in S4 (1) or Mn is the Clifford torus .In this paper, we generalize the results due to Chern, do Carmo and Kobayashi [1] to complete Riemannian manifolds.
2004 ◽
Vol 76
(3)
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pp. 489-497
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2007 ◽
Vol 09
(02)
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pp. 183-200
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2011 ◽
Vol 54
(1)
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pp. 67-75
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2011 ◽
Vol 22
(01)
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pp. 131-143
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1975 ◽
Vol 27
(3)
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pp. 610-617
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1983 ◽
Vol 26
(3)
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pp. 291-296
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2013 ◽
Vol 10
(06)
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pp. 1350025
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2009 ◽
Vol 51
(2)
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pp. 413-423
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2000 ◽
Vol 24
(1)
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pp. 43-48