Description
This text is about the mathematics of Riemannian holonomy groups and calibrated geometry. It is aimed at graduate students in mathematics and physics, and is written in a clear and accessible style. The text starts with basic geometry and covers seminal results in Riemannian holonomy, such as Yau's proof of the Calabi conjecture. It then moves on to calibrated geometry, discussing some of the most important results in the field. The text ends with some open problems, giving the reader a taste of the exciting and active research in this area.
This graduate level text covers an exciting and active area of research at the crossroads of several different fields in mathematics and physics. In mathematics it involves Differential Geometry, Complex Algebraic Geometry, Symplectic Geometry, and in physics String Theory and Mirror Symmetry. Drawing extensively on the author's previous work, the text explains the advanced mathematics involved simply and clearly to both mathematicians and physicists. Starting with the basic geometry of connections, curvature, complex and Khler structures suitable for beginning graduate students, the text covers seminal results such as Yau's proof of the Calabi Conjecture, and takes the reader all the way to the frontiers of current research in calibrated geometry, giving many open problems.
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