## Kyoto Journal of Mathematics

### A simple proof of the existence of tangent bicharacteristics for noneffectively hyperbolic operators

Tatsuo Nishitani

#### Abstract

The behavior of orbits of the Hamilton vector field $H_{p}$ of the principal symbol $p$ of a second-order hyperbolic differential operator is discussed. In our previous paper, assuming that $p$ is noneffectively hyperbolic on the doubly characteristic manifold $\Sigma$ of $p$, we have proved that if $H_{S}^{3}p=0$ on $\Sigma$ with the Hamilton vector field $H_{S}$ of some specified $S$, then there exists a bicharacteristic landing on $\Sigma$ tangentially. The aim of this paper is to provide a much more simple proof of this result since the previous proof was fairly long and rather complicated.

#### Article information

Source
Kyoto J. Math., Volume 55, Number 2 (2015), 281-297.

Dates
Revised: 9 January 2014
Accepted: 5 March 2014
First available in Project Euclid: 11 June 2015

https://projecteuclid.org/euclid.kjm/1433982756

Digital Object Identifier
doi:10.1215/21562261-2871758

Mathematical Reviews number (MathSciNet)
MR3356074

Zentralblatt MATH identifier
1320.35183

#### Citation

Nishitani, Tatsuo. A simple proof of the existence of tangent bicharacteristics for noneffectively hyperbolic operators. Kyoto J. Math. 55 (2015), no. 2, 281--297. doi:10.1215/21562261-2871758. https://projecteuclid.org/euclid.kjm/1433982756

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