Lectures on Calabi-Yau and Special Lagrangian Geometry by Dominic Joyce - PDF
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About this book :-
This book is 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 geometry. Yau Manifolds are special shapes (called "manifolds") in mathematics that are used in string theory. They are important because they help describe the extra dimensions of the universe that string theory suggests. These shapes have special properties, like being "Ricci-flat," meaning they don’t curve in a way that affects certain calculations.
Special Lagrangian Geometry looks at certain subspaces (smaller parts) of these Calabi-Yau manifolds. These subspaces have their own special rules, and they are important for understanding mirror symmetry in string theory, where one type of Calabi-Yau shape can be related to another in a unique way.
The book explains these ideas in a way that’s easy to follow for people who already know some higher-level math, like geometry and algebra. It’s meant for advanced students or researchers, but it also gives a peek into how these concepts relate to string theory, the branch of physics that looks at the fundamental nature of the universe. In short, the book helps us understand some complex mathematical shapes that have real-world applications in science, especially physics!.
Book Detail :-
This book has following details information.
Title:
Lectures on Calabi-Yau and Special Lagrangian Geometry by Dominic Joyce - PDF
Publisher:
arXiv
Year:
2002
Pages:
58
Type:
PDF
Language:
English
ISBN-10 #:
N\A
ISBN-13 #:
N\A
License:
N\A
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About Author :-
The author NA
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Book Contents :-
This book has following table of contents.
1. Introduction
2. Introduction to holonomy groups
3. Berger’s classification of holonomy groups
4. K¨ahler geometry and holonomy
5. The Calabi Conjecture and constructions of Calabi–Yau m-folds
6. Introduction to calibrated geometry
7. Special Lagrangian submanifolds in Cm
8. Constructions of SL m-folds in Cm
9. Compact SL m-folds in Calabi–Yau m-folds
10. Singularities of special Lagrangian m-folds
11. The SYZ Conjecture, and SL fibrations
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