English

A canonical way to deform a Lagrangian submanifold

dg-ga 2008-02-03 v2 Differential Geometry

Abstract

We derive some important geometric identities for Lagrangian submanifolds immersed in a K\"ahler manifold and prove that there exists a canonical way to deform a Lagrangian submanifold by a parabolic flow through a family of Lagrangian submanifolds if the ambient space is a Ricci-flat Calabi-Yau manifold.

Keywords

Cite

@article{arxiv.dg-ga/9605005,
  title  = {A canonical way to deform a Lagrangian submanifold},
  author = {Knut Smoczyk},
  journal= {arXiv preprint arXiv:dg-ga/9605005},
  year   = {2008}
}

Comments

16 pages, AMS-TeX. This replacement contains only minor changes. Corollary 2.8 was wrong and has been removed. Proposition 2.9 has been renamed into Proposition 2.8 and we also added a new theorem (Theorem 2.9). In addition the format and some of the questions and remarks have been altered. The author apologizes for any inconvenience