Gauss Map and Local Approach of Isoparametric Surfaces in Lorentz and Euclidean Space

ISSN: 2645-8845
Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 2018
Yayıncı: Fuat USTA

In this study, we determine the isoparametric surfaces and we give the Gauss map of these surfaces by semi symmetric matrix, in Lorentz space. Also we define any chord property and we show that the surfaces which have the chord property corresponds to isoparametric surfaces. Moreover, we consider the chord property locally and we give some examples in the Euclidean space.

Keywords:

Gauss map, Isoparametric surface Linear operator,

PDF

___

N. Kerzman, E.M. Stein, The Cauchy Kernel, the Szeg¨o Kernel, and the Riemann Mapping Function, Math.Ann. 236 (1978), 85-93.
H.P. Boas, A Geometric Characterization of the Ball and the Bochner-Martinelli Kernel, Math. Ann. 248 (1980), 275-278.
H.P. Boas, Spheres and Cylinders: A Local Geometric Characterization, Illinois Journal of Mathematics, 28(1) (1984), 120-124.
B. Wegner, A Differential Geometric Proof of the Local Geometric Characterization of Spheres and Cylinders by Boas, Mathematica Balkanica 2 (1988),294-295.
D.S. Kim, Y.H. Kim, New Characterizations of Spheres, Cylinders and W−Curves, Linear Algebra and Its Applications 432 (2010), 3002-3006.
Y. H. Kim, K. E. Lee, Surfaces of Euclidean 4-Space Whose Geodesics are W-Curves, Nihonkai Math. J., 4 (1993), 221-232.
B. O’Neill, Semi-Riemann Geometry with Applications to Relativity, Academic Press. Inc., (1983).
E. Öztürk, Y. Yaylı, W-Curves In Lorentz-Minkowski Space, Mathematical Sciences and Applications E-Notes, 5(2) (2017), 76-88.
C. Ekici, E. Ozüsağlam, M. Çimdiker, E. Öztürk, On The Curvatures of Viviani Ruled Surface, Ciencia e Tecnica Vitivinicola, 29(7) (2014), 449-475