MIT Libraries logoDSpace@MIT

MIT
View Item 
  • DSpace@MIT Home
  • MIT Libraries
  • MIT Theses
  • Doctoral Theses
  • View Item
  • DSpace@MIT Home
  • MIT Libraries
  • MIT Theses
  • Doctoral Theses
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Calibrations and minimal Lagrangian submanifolds

Author(s)
Goldstein, Edward, 1977-
Thumbnail
DownloadFull printable version (9.193Mb)
Other Contributors
Massachusetts Institute of Technology. Dept. of Mathematics.
Advisor
Tomasz S. Mrowka.
Terms of use
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. http://dspace.mit.edu/handle/1721.1/7582
Metadata
Show full item record
Abstract
This thesis will be concerned with the geometry of minimal submanifolds in certain Riemannian manifolds which possess some special geometric structure. Those Riemannian manifolds will fall into one of the following categories: 1) A Riemannian manifold M with a calibrating k-form n7. We will derive some intrinsic volume comparison results for calibrated submanifolds of M and give some basic applications to their intrinsic geometry. 2) A Kahler n-fold M with a nowhere vanishing holomorphic (n, 0)-form (we will call'M an almost Calabi-Yau manifold). We will study the geometry of Special Lagrangian submanifolds on M and the global properties of their moduli-space. We will exhibit an example of a compact, simply connected almost Calabi-Yau threefold, which admits a Special Lagrangian torus fibration. We will also show how to construct Special Lagrangian fibrations on non-compact almost Calabi-Yau manifolds using torus actions and give numerous examples of such fibrations. 3) A Kahler-Einstein manifold M with non-zero scalar curvature. We will study the geometry of minimal Lagrangian submanifolds in M and their interaction with the geometry of M. We will also construct some new families of minimal Lagrangian submanifolds in toric Kahler-Einstein manifolds. 4) A Riemannian 7-manifold with holonomy G2. We will construct some new examples of coassociative submanifolds on complete Riemannian 7-manifolds with holonomy G2 via group actions.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001.
 
Includes bibliographical references (p. 119-122).
 
Date issued
2001
URI
http://hdl.handle.net/1721.1/8639
Department
Massachusetts Institute of Technology. Department of Mathematics
Publisher
Massachusetts Institute of Technology
Keywords
Mathematics.

Collections
  • Doctoral Theses

Browse

All of DSpaceCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

My Account

Login

Statistics

OA StatisticsStatistics by CountryStatistics by Department
MIT Libraries
PrivacyPermissionsAccessibilityContact us
MIT
Content created by the MIT Libraries, CC BY-NC unless otherwise noted. Notify us about copyright concerns.