Abstract
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.
Citation
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. https://doi.org/10.2969/jmsj/06610123
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