Metric Structures on Fibered Manifolds Through Partitions of Unity


Kadıoğlu H. , Fisher R.

New Trends in Math. Sci., cilt.4, ss.266-272, 2016 (Diğer Kurumların Hakemli Dergileri)

  • Cilt numarası: 4 Konu: 2
  • Basım Tarihi: 2016
  • Dergi Adı: New Trends in Math. Sci.
  • Sayfa Sayıları: ss.266-272

Özet

The notion of partitions of unity is extremely useful as it allows one to extend local constructions on Euclidean patches to global ones. It is widely used in many fields in mathematics. Therefore, prolongation of this useful tool to another manifold may help constructing many geometric structures. In this paper, we construct a partition of unity on a fiber bundle by using a given partition of unity on the base manifold. On the other hand we show that the converse is also possible if it is a vector bundle. As an application, we define a Riemannian metric on the fiber bundle by using induced partition of unity on the fiber bundle.