Generalized Minkowski space with changing shape

详细信息    查看全文

• 作者：á. G. Horváth (1)
  
• 关键词：46C50 ; 46C20 ; 53B40 ; Generalized space ; time model ; Normed space ; Minkowski space ; Random and stochastic models
• 刊名：Aequationes Mathematicae
• 出版年：2014
• 出版时间：June 2014
• 年：2014
• 卷：87
• 期：3
• 页码：337-377
• 全文大小：
• 参考文献：1. Bandt C., Baraki G.: Metrically invariant measures on locally homogeneous spaces and hyperspaces. Pacific. J. Math. 121, 13-8 (1986) CrossRef
  2. Dubrovin B.A., Fomenko A.T., Novikov S.P.: Modern Geometry-methods and applications, Part I. The geometry of surfaces, transformation groups, and fields. Springer, New York (1992)
  3. Dawis, M.W., Moussong, G.: Notes on nonpositively curved polyhedra Bolyai Society Mathematical Studies, 8, Budapest, (1999)
  4. Giles J.R.: Classes of semi-inner-product spaces. Trans. Amer. Math.Soc. 129/3, 436-46 (1967) CrossRef
  5. Gohberg I., Lancester P., Rodman L.: Indefinite linear algebra and applications. Birkh?user, Basel-Boston-Berlin (2005)
  6. Hoffmann L.M.: Measures on the space of convex bodies. Adv. Geom. 10, 477-86 (2010) CrossRef
  7. Horváth á.G.: Semi-indefinite inner product and generalized Minkowski spaces. J. Geometry Physics 60, 1190-208 (2010)
  8. Horváth á.G.: Premanifolds. Note di Math. 31/2, 17-1 (2011)
  9. Horváth á.G.: Normally distributed probability measure on the metric space of norms. Acta Mathematica Scientia 33(5), 1231-242 (2013)
  10. Gruber, P.M., Wills, J. M. (Hrsg.) Handbook of Convex Geometry. Volume A,B, North Holland, Amsterdam (1993)
  11. Gruber P.M.: Convex and discrete geometry. Springer, Berlin, Heidelberg (2007)
  12. Kolmogorov, A.N.: Basic concepts of probability theory. (in russian) Izgatelctvo “Nauka-(1974)
  13. Lumer G.: Semi-inner product spaces. Trans. Amer. Math. Soc. 100, 29-3 (1961) CrossRef
  14. Martini H., Swanepoel K., Weiss G.: The geometry of Minkowski spaces—a survey. Part I. Expositiones Mathematicae 19, 97-42 (2001) CrossRef
  15. Martini H., Swanepoel K.: The geometry of Minkowski spaces—a survey. Part II.. Expo. Math. 22(2), 93-44 (2004) CrossRef
  16. Minkowski, H.: Raum und Zeit Jahresberichte der Deutschen Mathematiker-Vereinigung, Leipzig (1909)
  17. Schneider R.: Convex bodies: the Brunn-Minkowski theory. Cambridge University Press, Cambridge (1993) CrossRef
  
• 作者单位：á. G. Horváth (1)
  
  1. Department of Geometry, Mathematical Institute, Budapest University of Technology and Economics, 1521, Budapest, Hungary
  
• ISSN：1420-8903

文摘

In earlier papers we changed the concept of the inner product to a more general one, to the so-called Minkowski product. This product changes on the tangent space hence we could investigate a more general structure than a Riemannian manifold. Particularly interesting such a model is when the negative direct component has dimension one and the model shows a certain space-time character. We will discuss this case here. We give a deterministic and a non-deterministic (random) variant of such a model. As we showed, the deterministic model can be defined also with a “shape function-