Nearly-Kähler 6-manifolds of cohomogeneity two : local theory
Abstract/Contents
- Abstract
- We study nearly-Kahler 6-manifolds equipped with a cohomogeneity-two Lie group action for which each principal orbit is coisotropic. If the metric is complete, this last condition is automatically satisfied. We will show that the acting Lie group must be 4-dimensional and non-abelian. We partition the class of such nearly-Kahler structures into three types (called I, II, III) and prove a local existence and generality result for each type. Metrics of Types I and II are shown to be incomplete. We also derive a quasilinear elliptic PDE system on a Riemann surface that nearly-Kahler structures of Type I must satisfy. Finally, we remark on a relatively simple one-parameter family of Type III structures that turn out to be incomplete metrics cohomogeneity-one under the action of a larger group.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2018; ©2018 |
| Publication date | 2018; 2018 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Madnick, Jesse Ochs |
|---|---|
| Degree supervisor | Mazzeo, Rafe |
| Degree supervisor | Schoen, Richard (Richard M.) |
| Thesis advisor | Mazzeo, Rafe |
| Thesis advisor | Schoen, Richard (Richard M.) |
| Thesis advisor | Bryant, Robert L |
| Degree committee member | Bryant, Robert L |
| Associated with | Stanford University, Department of Mathematics. |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Jesse Ochs Madnick. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis Ph.D. Stanford University 2018. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2018 by Jesse Ochs Madnick
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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