Bulletin of the Australian Mathematical
Society
Bull. Austral. Math. Soc.
0004-9727
ALNBAB
2005
72
3
10.wxyz/CV72P3
http://www.austms.org.au/Publ/Bulletin/V72P3/
Examples and classification of Riemannian submersions
satisfying a basic equality
Bang-Yen Chen
13 February 2006
2006
2
13
391
402
723-5198-Chen-2005
10.wxyz/C2005V72P3p391
http://www.austms.org.au/Publ/Bulletin/V72P3/723-5198-Chen/
In an earlier article we obtain a sharp inequality
for an arbitrary isometric immersion from a Riemannian
manifold admitting a Riemannian submersion with totally
geodesic fibres into a unit sphere. In this article we
investigate the immersions which satisfy the equality case of
the inequality. As a by-product, we discover a new
characterisation of Cartan hypersurface in $S^4$.
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