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January, 2014 Degeneracy locus of critical points of the distance function on a holomorphic foliation
Toshikazu ITO, Bruno SCÁRDUA, Yoshikazu YAMAGISHI
J. Math. Soc. Japan 66(1): 123-137 (January, 2014). DOI: 10.2969/jmsj/06610123


We study the geometry of transversality of holomorphic foliations of codimension one in ${\mathbb C}^n$ with spheres, from a viewpoint of dynamics of anti-holomorphic maps in the projective space. A point of non-degenerate contact of a leaf with a sphere is a hyperbolic fixed point of the corresponding dynamics. Around a point of degenerate contact, the intersection of branches of the variety of contacts is described as a bifurcation diagram of a neutral fixed point of dynamics. The Morse index for the distance function from the origin is computed as the complex dimension of an unstable manifold.


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Toshikazu ITO. Bruno SCÁRDUA. Yoshikazu YAMAGISHI. "Degeneracy locus of critical points of the distance function on a holomorphic foliation." J. Math. Soc. Japan 66 (1) 123 - 137, January, 2014.


Published: January, 2014
First available in Project Euclid: 24 January 2014

zbMATH: 1288.32044
MathSciNet: MR3161395
Digital Object Identifier: 10.2969/jmsj/06610123

Primary: 32S65
Secondary: 37F75

Keywords: anti-holomorphic , Foliation , Morse index , singularity , transversality

Rights: Copyright © 2014 Mathematical Society of Japan


Vol.66 • No. 1 • January, 2014
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