Journal of the Mathematical Society of Japan

Examples of infinitesimally flexible 3-dimensional hyperbolic cone-manifolds


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Weiss and, independently, Mazzeo and Montcouquiol recently proved that a 3-dimensional hyperbolic cone-manifold (possibly with vertices) with all cone angles less than 2π is infinitesimally rigid. On the other hand, Casson provided 1998 an example of an infinitesimally flexible cone-manifold with some of the cone angles larger than 2π. In this paper several new examples of infinitesimally flexible cone-manifolds are constructed. The basic idea is that the double of an infinitesimally flexible polyhedron is an infinitesimally flexible cone-manifold. With some additional effort, we are able to construct infinitesimally flexible cone-manifolds without vertices and with all cone angles larger than 2π.

Article information

J. Math. Soc. Japan, Volume 63, Number 2 (2011), 581-598.

First available in Project Euclid: 25 April 2011

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Zentralblatt MATH identifier

Primary: 57M50: Geometric structures on low-dimensional manifolds 52B10: Three-dimensional polytopes

hyperbolic cone-manifold infinitesimal isometry Pogorelov map


IZMESTIEV, Ivan. Examples of infinitesimally flexible 3-dimensional hyperbolic cone-manifolds. J. Math. Soc. Japan 63 (2011), no. 2, 581--598. doi:10.2969/jmsj/06320581.

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