Discrete Symmetries of Complete Intersection Calabi–Yau Manifolds

Maximal Unipotent Monodromy for Complete Intersection CY Manifolds

The computations that are suggested by String Theory in the B model requires the existence of degenerations of CY manifolds with maximum unipotent monodromy. In String Theory such a point in the moduli space is called a large radius limit (or large complex structure limit). In this paper we are going to construct one parameter families of n dimensional Calabi-Yau manifolds, which are complete i...

Symmetries of Contact Metric Manifolds

We study the Lie algebra of infinitesimal isometries on compact Sasakian and K–contact manifolds. On a Sasakian manifold which is not a space form or 3– Sasakian, every Killing vector field is an infinitesimal automorphism of the Sasakian structure. For a manifold with K–contact structure, we prove that there exists a Killing vector field of constant length which is not an infinitesimal automor...

Symmetries of Discrete Objects

Symmetries and Motions in Manifolds

In these lectures the relations between symmetries, Lie algebras, Killing vectors and Noether’s theorem are reviewed. A generalisation of the basic ideas to include velocity-dependend co-ordinate transformations naturally leads to the concept of Killing tensors. Via their Poisson brackets these tensors generate an a priori infinitedimensional Lie algebra. The nature of such infinite algebras is...

Hidden symmetries and arithmetic manifolds

Let M be a closed, locally symmetric Riemannian manifold of nonpositive curvature with no local torus factors; for example take M to be a hyperbolic manifold. Equivalently, M = K\G/Γ where G is a semisimple Lie group and Γ is a cocompact lattice in G. For simplicity, we will always assume that Γ is irreducible, or equivalently that M is not finitely covered by a smooth product; we will also ass...