Calabi-Yau Manifolds and Related Geometries
Contributors: Geir Ellingsrud (Editor); Loren Olson (Editor); Kristian Ranestad (Editor); Stein A. Stromme (Editor)
Edition: 1 edition
Publisher: Springer
Published: January 17, 2003
Language: eng
Format: Paperback
Number of pages: 239
ISBN-13: 9783540440598
Subjects: Differential & Riemannian geometry; Mathematics; Algebra - General; Riemannian Manifolds; Science; Mathematical Physics; Science/Mathematics; Geometry - Differential; Calabi-Yau manifolds; Geometry - Algebraic; Mathematics / Geometry / Algebraic; hyperkahler manifolds; mirror symmetry; special lagrangian submanifolds
First sentence: We begin by giving some background from differential and Riemannian geometry, principally to establish notation, and move on to discuss connections on vector bundles, parallel transport, and the definition of holonomy groups.
Description: This book is an expanded version of lectures given at a summer school on symplectic geometry in Nordfjordeid, Norway, in June 2001. The unifying feature of the book is an emphasis on Calabi-Yau manifolds. The first part discusses holonomy groups and calibrated submanifolds, focusing on special Lagrangian submanifolds and the SYZ conjecture. The second studies Calabi-Yau manifolds and mirror symmetry, using algebraic geometry. The final part describes compact hyperkahler manifolds, which have a geometric structure very closely related to Calabi-Yau manifolds. The book is an introduction to a very active field of research, on the boundary between mathematics and physics. It is aimed at graduate students and researchers in geometry and string theory and intended as an introductory text, requiring only limited background knowledge. Proofs or sketches are given for many important results. Moreover, exercises are provided.