Vector fields on certain quotients of complex Stiefel manifolds

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...

On the Stiefel-whitney Numbers of Complex Manifolds and of Spin Manifolds

Proof. First consider the following example of the Conner-Floyd theorem. Let H,,,,,(C) denote a non-singular hypersurface of degree (1,l) in the product P,,,(C) x P.(C). b terms of homogeneous co-ordinates (wO, . . . , w,) and (z,,, . . . , .z”) with m 5 n this hypersurface can be defined as the locus w,,z, + wlzl + . . . + w,,,z, = 0. It can also be thought of as a P,_,(C)-bundle over P,(C).] ...

Harmonic-Killing vector fields on Kähler manifolds

In a previous paper we have considered the harmonicity of local infinitesimal transformations associated to a vector field on a (pseudo)-Riemannian manifold to characterise intrinsi-cally a class of vector fields that we have called harmonic-Killing vector fields. In this paper we extend this study to other properties, such as the pluriharmonicity and the α-pluriharmonicity (α harmonic 2-form) ...

Rolling Stiefel manifolds

In this paper rolling maps for real Stiefel manifolds are studied. Real Stiefel manifolds being the set of all orthonormal k-frames of an n-dimensional real Euclidean space are compact manifolds. They are considered here as rigid bodies embedded in a suitable Euclidean space such that the corresponding Euclidean group acts on the rigid body by rotations and translations in the usual way. We der...

Notes on Optimization on Stiefel Manifolds