Question

hi,

does anybody know a good book on calabi yau manifolds (i am a beginner) ? thanks in advance

lois

Answer 1

Depending on how much of a beginner you are, you could begin by reading Barth-Hulek-Peters-Van de Ven paying particular attention to the section on K3 surfaces (which are 2-(complex)-dimensional Calabi-Yaus):

http://www.springer.com/mathematics/algebra/book/978-3-540-00832-3

For an overview, you could try:

http://www.scholarpedia.org/article/Calabi-Yau_manifold

Other good and possibly relevant books include:

Besse, Arthur L. (1987), Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 10, Berlin, New York: Springer-Verlag,

Gross, M.; Huybrechts, D.; Joyce, Dominic (2003), Calabi–Yau manifolds and related geometries, Universitext, Berlin, New York: Springer-Verlag,

Hübsch, Tristan (1994), Calabi–Yau Manifolds: a Bestiary for Physicists, Singapore, New York: World Scientific.

Answer 2

I would also add the following book:

Dominic Joyce, Compact Manifolds with Special Holonomy

The early parts of the book include an introduction to the Riemannian geometry of Calabi-Yau manifolds. It also includes a proof of the Calabi conjecture.