Manifolds with Many Rarita–Schwinger Fields

Manifolds With Many Hyperbolic Planes

We construct examples of complete Riemannian manifolds having the property that every geodesic lies in a totally geodesic hyperbolic plane. Despite the abundance of totally geodesic hyperbolic planes, these examples are not locally homogenous.

Manifolds with Many Complex Structures

construction of vector fields with positive lyapunov exponents

in this thesis our aim is to construct vector field in r3 for which the corresponding one-dimensional maps have certain discontinuities. two kinds of vector fields are considered, the first the lorenz vector field, and the second originally introced here. the latter have chaotic behavior and motivate a class of one-parameter families of maps which have positive lyapunov exponents for an open in...

Calabi–Yau Manifolds with B–Fields

In recent work N. Hitchin introduced the concept of “generalised geometry”. The key feature of generalised structures is that that they can be acted on by both diffeomorphisms and 2–forms, the so–called B–fields. In this lecture, we give a basic introduction and explain some of the fundamental ideas. Further, we discuss some examples of generalised geometries starting from the usual notion of a...

Vector Fields on Manifolds

where n = dim M and 6» = ith Betti number of M ( = dim of Hi(M; Q)). Thus the geometric property of M having a nonzero vector field is expressed in terms of the algebraic invariant xM. We will discuss extensions of this idea to vector ^-fields, fields of ^-planes, and foliations of manifolds. All manifolds considered will be connected, smooth and without boundary; all maps will be continuous. F...