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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Solving for Volume-Minimizing Cycles in G2-Manifolds

Jauregui, Jeff Loren 01 May 2005 (has links)
M-theory, a generalization of string theory, motivates the search for examples of volume minimizing cycles in Riemannian manifolds of G2 holonomy. Methods of calibrated geometry lead to a system of four coupled nonlinear partial differential equations whose solutions correspond to associa- tive submanifolds of R7, which are 3-dimensional and minimize volume in their real homology classes. Several approaches to finding new solutions are investigated, the most interesting of which exploits the quaternionic structure of the PDE system. A number of examples of associative 3-planes are explicitly given; these may possibly be projected to nontrivial volume minimizing cycles in, for example, the G2-manifold R6 × S1.

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