Rigidity and invariance properties of certain geometric frameworks
Name
50500348-MIT.pdf
Description
Full printable version
Size
3.08 MB
Format
Adobe PDF
Checksum (MD5)
7d859989fed184ca5c9af8beb6aa4e4b
Author(s)
Zhang, Lizhao, 1973-
Advisor(s)
Daniel J. Kleitman.
Date Issued
2002
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2002.
Includes bibliographical references (leaves 59-60).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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