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Autor(en): 
  • Zhongmin Shen
  • Differential Geometry of Spray and Finsler Spaces 
     

    (Buch)
    Dieser Artikel gilt, aufgrund seiner Grösse, beim Versand als 3 Artikel!


    Übersicht

    Auf mobile öffnen
     
    Lieferstatus:   Auf Bestellung (Lieferzeit unbekannt)
    Veröffentlichung:  Dezember 2010  
    Genre:  Schulbücher 
     
    Applications of Mathematics / Applied mathematics / Biomathematics / C / Calculus of variations / Calculus of Variations and Optimal Control; Optimization / Calculus of Variations and Optimization / Computational biology / bioinformatics / Differential calculus & equations / Differential equations / Differential Geometry / Engineering mathematics / Mathematical and Computational Biology / Mathematics and Statistics / Maths for scientists / Optimization / Ordinary Differential Equations
    ISBN:  9789048156733 
    EAN-Code: 
    9789048156733 
    Verlag:  Springer Nature EN 
    Einband:  Kartoniert  
    Sprache:  English  
    Dimensionen:  H 235 mm / B 155 mm / D  
    Gewicht:  421 gr 
    Seiten:  258 
    Zus. Info:  Previously published in hardcover 
    Bewertung: Titel bewerten / Meinung schreiben
    Inhalt:
    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.
      
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