Lectures on Exterior Differential Systems
by M. Kuranishi
Publisher: Tata Institute of Fundamental Research 1962
Number of pages: 117
Contents: Parametrization of sets of integral submanifolds (Regular linear maps, Germs of submanifolds of a manifold); Exterior differential systems (Differential systems with independent variables); Prolongation of Exterior Differential Systems.
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by Dominic Joyce - arXiv
An introduction to Calabi-Yau manifolds and special Lagrangian submanifolds from the differential geometric point of view, followed by recent results on singularities of special Lagrangian submanifolds, and their application to the SYZ Conjecture.
by Li Ma - Tsinghua University
Contents: Ricci-Hamilton flow on surfaces; Bartz-Struwe-Ye estimate; Hamilton's another proof on S2; Perelman's W-functional and its applications; Ricci-Hamilton flow on Riemannian manifolds; Maximum principles; Curve shortening flow on manifolds.
by Liviu I. Nicolaescu - University of Notre Dame
This is arguably one of the deepest and most beautiful results in modern geometry, and it is surely a must know for any geometer / topologist. It has to do with elliptic partial differential operators on a compact manifold.
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Contents: Affine connections and transformations; Symmetric spaces; Orthogonal symmetric Lie algebras; Examples; Noncompact symmetric spaces; Compact semisimple Lie groups; Hermitian symmetric spaces; Classification of real simple Lie algebras.