Rigidity and invariance properties of certain geometric frameworks

Given a degenerate (n + 1)-simplex in a n-dimensional Euclidean space Rn, which is embedded in a (n + 1)-dimensional Euclidean space Rn+l. We allow all its vertices to have continuous motion in the space, either in Rn+l or restricted in Rn. For a given k, based on certain rules, we separate all its k-faces into 2 groups. During the motion, we give the following restriction: the volume of the k-faces in the 1st group can not increase (these faces are called "k-cables"); the volume of the k-faces in the 2nd group can not decrease ("k-struts"). We will prove that, under more conditions, all the volumes of the k-faces will be preserved for any sufficiently small motion. We also partially generalize the above result to spherical space Sn and hyperbolic space Hn.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2002

Author dc:creator

• Zhang, Lizhao, 1973-

Advisor dc:contributor.advisor

• Daniel J. Kleitman.

• Mathematics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/8337

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/8337