1,865 research outputs found
Calibrated embeddings in the special Lagrangian and coassociative cases
Every closed, oriented, real analytic Riemannian 3-manifold can be
isometrically embedded as a special Lagrangian submanifold of a Calabi-Yau
3-fold, even as the real locus of an antiholomorphic, isometric involution.
Every closed, oriented, real analytic Riemannian 4-manifold whose bundle of
self-dual 2-forms is trivial can be isometrically embedded as a coassociative
submanifold in a G_2-manifold, even as the fixed locus of an anti-G_2
involution.
These results, when coupled with McLean's analysis of the moduli spaces of
such calibrated submanifolds, yield a plentiful supply of examples of compact
calibrated submanifolds with nontrivial deformation spaces.Comment: AMS-TeX v. 2.1, 26 pages, uses amsppt.sty (2.1h), minor typos
correcte
Rigidity and quasi-rigidity of extremal cycles in Hermitian symmetric spaces
I use local differential geometric techniques to prove that the algebraic
cycles in certain extremal homology classes in Hermitian symmetric spaces are
either rigid (i.e., deformable only by ambient motions) or quasi-rigid (roughly
speaking, foliated by rigid subvarieties in a nontrivial way).
These rigidity results have a number of applications: First, they prove that
many subvarieties in Grassmannians and other Hermitian symmetric spaces cannot
be smoothed (i.e., are not homologous to a smooth subvariety). Second, they
provide characterizations of holomorphic bundles over compact Kahler manifolds
that are generated by their global sections but that have certain polynomials
in their Chern classes vanish (for example, c_2 = 0, c_1c_2 - c_3 = 0, c_3 = 0,
etc.).Comment: 113 pages, 6 figures, latex2e with packages hyperref, amsart,
graphicx. For Version 2: Many typos corrected, important references added
(esp. to Maria Walters' thesis), several proofs or statements improved and/or
correcte
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