Title of the course: Lectures on calibrations and generalized duality
Instructor: Associate Professor Kurando Baba
Institution: Tokyo University of Science
Dates: 6-12 January 2020
Prerequisites: Linear Algebra, Riemannian Geometry (not a must but preferable)
Level: Graduate Advanced undergraduate
Abstract: In this lecture series we discuss calibrated geometry in the view point of Lie groups actions on symmetric spaces. Concrete examples of calibrations given by Harvey-Lawson are invariant under the action of the holonomy groups of Riemannian manifolds, which give Lie group actions on Grassmannian manifolds with geometrically nice properties. We also explain constructions of calibrated submanifolds. In particular, we give special Lagrangian submanifolds in Stenzel spaces by using moment map techniques. The calibrated geometry was generalized by Mealy in the pseudo-Riemannian geometry category. We give a correspondence between Harvey-Lawson’s calibrations and Mealy’s calibrations by a generalization of the duality in symmetric spaces.
Textbook and References:
1. M. Arai and K. Baba, Special Lagrangian submanifolds and cohomogeneity one actions on the projective spaces, Tokyo J. Math. 42 (2019), 255-284.
2. R. Harvey and H. B. Lawson, Jr., Calibrated geometries, Acta Math, 148 (1982), 47-157.
3. S. Helgason, Differential geometry, Lie groups, and symmetric spaces, Academic Press (1979).
4. J. Mealy, Volume maximization in semi-Riemannian manifolds, Indiana Univ. Math. J. 40 (1991) 793-814.
Language: EN