Graduation Year
2005
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Weiqing Gu
Reader 2
Jon T. Jacobsen
Abstract
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.
Recommended Citation
Jauregui, Jeff Loren, "Solving for Volume-Minimizing Cycles in G2-Manifolds" (2005). HMC Senior Theses. 170.
https://scholarship.claremont.edu/hmc_theses/170
Thesis Proposal
jauregui.jpg (25 kB)
Picture of Jeff Jauregui
jauregui-final-talk.pdf (1099 kB)
HMC Presentation Days 2005 Slides
