Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 57, Number 1 (2005), 1-20.
A conjecture in relation to Loewner's conjecture
Let be a smooth function of two variables , and for each positive integer , let be a symmetric tensor field of type defined by and a finitely many-valued one-dimensional distribution obtained from : for example, is the one-dimensional distribution defined by the gradient vector field of ; consists of two one-dimensional distributions obtained from one-dimensional eigenspaces of Hessian of . In the present paper, we shall study the behavior of around its isolated singularity in ways which appear in --. In particular, we shall introduce and study a conjecture which asserts that the index of an isolated singularity with respect to is not more than one.
J. Math. Soc. Japan, Volume 57, Number 1 (2005), 1-20.
First available in Project Euclid: 13 October 2006
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ANDO, Naoya. A conjecture in relation to Loewner's conjecture. J. Math. Soc. Japan 57 (2005), no. 1, 1--20. doi:10.2969/jmsj/1160745810. https://projecteuclid.org/euclid.jmsj/1160745810