Metric Structures on Fibered Manifolds Through Partitions of Unity

Kadıoğlu H., Fisher R.

New Trends in Math. Sci., cilt.4, sa.2, ss.266-272, 2016 (Hakemli Dergi)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 4 Sayı: 2
  • Basım Tarihi: 2016
  • Dergi Adı: New Trends in Math. Sci.
  • Derginin Tarandığı İndeksler: Other Indexes
  • Sayfa Sayıları: ss.266-272
  • Yıldız Teknik Üniversitesi Adresli: Evet

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.