Title: An exotic totally real minimal immersion of S^3 in CP^3 and its characterisation
Authors: Chen, Bang-Yen ×
Dillen, Franki
Verstraelen, Leopold
Vrancken, Luc #
Issue Date: 1996
Publisher: Royal soc edinburgh
Series Title: Proceedings of the royal society of edinburgh section a-mathematics vol:126 pages:153-165
Abstract: In a previous paper, B.-Y. Chen defined a Riemannian invariant delta by subtracting from the scalar curvature at every point of a Riemannian manifold the smallest sectional curvature at that point, and proved, for a submanifold of a real space form, a sharp inequality between delta and the mean curvature function. In this paper, we extend this inequality to totally real submanifolds of a complex space form. As a consequence, we obtain a metric obstruction for a Riemannian manifold M(n) to admit a minimal totally real (i.e. Lagrangian) immersion into a complex space form of complex dimension n. Next we investigate three-dimensional submanifolds of the complex projective space CP3 which realise the equality in the inequality mentioned above. In particular, we construct and characterise a totally real minimal immersion of S-3 in CP3.
ISSN: 0308-2105
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Geometry Section
× corresponding author
# (joint) last author

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