Differential Geometry of Spray and Finsler Spaces

af


Differential Geometry of Spray and Finsler Spaces
Format:
Bog, hardback
Udgivelsesdato:
01-03-2001
Sprog:
Engelsk
  • Beskrivelse
  • Yderligere info
  • Anmeldelser

In this book we study sprays and Finsler metrics. Roughly speaking, a spray on a manifold consists of compatible systems of second-order ordinary differential equations. A Finsler metric on a manifold is a family of norms in tangent spaces, which vary smoothly with the base point. Every Finsler metric determines a spray by its systems of geodesic equations. Thus, Finsler spaces can be viewed as special spray spaces. On the other hand, every Finsler metric defines a distance function by the length of minimial curves. Thus Finsler spaces can be viewed as regular metric spaces. Riemannian spaces are special regular metric spaces. In 1854, B. Riemann introduced the Riemann curvature for Riemannian spaces in his ground-breaking Habilitationsvortrag. Thereafter the geometry of these special regular metric spaces is named after him. Riemann also mentioned general regular metric spaces, but he thought that there were nothing new in the general case. In fact, it is technically much more difficult to deal with general regular metric spaces. For more than half century, there had been no essential progress in this direction until P. Finsler did his pioneering work in 1918. Finsler studied the variational problems of curves and surfaces in general regular metric spaces. Some difficult problems were solved by him. Since then, such regular metric spaces are called Finsler spaces. Finsler, however, did not go any further to introduce curvatures for regular metric spaces. He switched his research direction to set theory shortly after his graduation.

Andre udgaver:

Bog, hæftet
E-bog, PDF

Vis mereVis mindre

ISBN13:
9780792368687
Vægt:
558 g
Dybde:
16 mm
Bredde:
156 mm
Højde:
234 mm
Forlag:
Springer
Format:
Hardback

Vis mereVis mindre

Vis mereVis mindre

Differential Geometry of Spray and Finsler Spaces

af

  • Leveringstid 4-6 hverdage
  • Forventet levering 24-06-2019

på lager

Fandt du ikke hvad du søgte?

Hvis denne bog ikke er noget for dig, kan du benytte kategorierne nedenfor til at finde andre titler. Klik på en kategori for at se lignende bøger.