
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 Kähler 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.
This text investigates the intersection of Riemannian holonomy groups and calibrated geometry, providing a comprehensive framework for understanding their roles in modern mathematics and theoretical physics. Dominic Joyce, a prominent mathematician, leverages his extensive research background to synthesize complex topics such as Kähler structures and the Calabi Conjecture. The book serves as a bridge between foundational geometric principles and advanced research frontiers, specifically targeting the needs of graduate-level students and practitioners in both mathematics and physics.
What You Will Find
Experts recognize this work as a rigorous and authoritative resource for those specializing in geometric analysis and string theory. Readers frequently note the high level of technical density, which requires a strong background in differential geometry to fully comprehend the presented proofs and theoretical developments.
Page Count:
314
Publication Date:
2007-01-01
Publisher:
FisicalBook
ISBN-10:
019921560X
ISBN-13:
9780199215607
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