Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions
1999 ◽
Vol 41
(1)
◽
pp. 33-41
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Keyword(s):
First we define the notion of k-Ricci curvature of a Riemannian n-manifold. Then we establish sharp relations between the k-Ricci curvature and the shape operator and also between the k-Ricci curvature and the squared mean curvature for a submanifold in a Riemannian space form with arbitrary codimension. Several applications of such relationships are also presented.
2002 ◽
Vol 72
(2)
◽
pp. 247-256
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Keyword(s):
2002 ◽
Vol 29
(12)
◽
pp. 719-726
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Keyword(s):
2001 ◽
Vol 64
(2)
◽
pp. 201-212
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Keyword(s):
Keyword(s):
2006 ◽
Vol 56
(10)
◽
pp. 2177-2188
◽
2016 ◽
Vol 13
(07)
◽
pp. 1650094
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2003 ◽
Vol 67
(1)
◽
pp. 51-65
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Keyword(s):
Keyword(s):
2005 ◽
Vol 2005
(10)
◽
pp. 1621-1632
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