ON EULER'S THEOREM IN SEMI-EUCLIDEAN SPACES E-v(n+1)


Coken A. C.

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, cilt.8, ss.1117-1129, 2011 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 8 Konu: 5
  • Basım Tarihi: 2011
  • Doi Numarası: 10.1142/s0219887811005579
  • Dergi Adı: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
  • Sayfa Sayıları: ss.1117-1129

Özet

In this paper, we study Euler's theorem for semi-Euclidean hypersurfaces in the semi-Euclidean spaces E-v(n+1). We obtain an analog of the well-known Euler's theorem for semi-Euclidean hypersurfaces in the semi-Euclidean spaces E-v(n+1). Then we give corollaries of Euler's theorem concerning conjugate and asymptotic directions. After that, we express Euler's theorem and its corollaries for hypersurfaces in the Euclidean space E-m in the case n = m - 1, v = 0. In addition, we give the well-known Euler's theorem and its corollaries for surfaces in the case n = 2, v = 0, for Lorentz surfaces in the case n = 2, v = 1 and for hypersurfaces in Lorentz spaces in the case n = m-1, v = 1.