Filtreler

2014 - 20176
Filtreleri Sıfırla

Ayarlar

Yazar: Bektaş, Burcu ×

Arama Sonuçları

Listeleniyor 1 - 6 / 6
  • Küçük Resim
    Yayın
    Pseudo-spherical submanifolds with 1-type pseudo-spherical gauss map
    (Birkhauser Verlag AG, 2016-05-28) Bektaş, Burcu; Canfes, Elif Özkara; Dursun, Uğur
    In this work, we study pseudo-Riemannian submanifolds of a pseudo-sphere with 1-type pseudo-spherical Gauss map. First, we classify Lorentzian surfaces in a 4-dimensional pseudo-sphere (Formula presented.) with index s, (Formula presented.), and having harmonic pseudo-spherical Gauss map. Then we give a characterization theorem for pseudo-Riemannian submanifolds of a pseudo-sphere (Formula presented.) with 1-type pseudo-spherical Gauss map, and we classify spacelike surfaces and Lorentzian surfaces in the de Sitter space (Formula presented.) with 1-type pseudo-spherical Gauss map. Finally, according to the causal character of the mean curvature vector we obtain the classification of submanifolds of a pseudo-sphere having 1-type pseudo-spherical Gauss map with nonzero constant component in its spectral decomposition.
  • Küçük Resim
    Yayın
    Timelike rotational surfaces of elliptic, hyperbolic and parabolic types in minkowski space E-1(4) with pointwise 1-type gauss map
    (University of Nis, 2015) Bektaş, Burcu; Dursun, Uğur
    In this work, we focus on a class of timelike rotational surfaces in Minkowski space E-1(4) with 2-dimensional axis. There are three types of rotational surfaces with 2-dimensional axis, called rotational surfaces of elliptic, hyperbolic or parabolic type. We obtain all flat timelike rotational surface of elliptic and hyperbolic types with pointwise 1-type Gauss map of the first and second kind. We also prove that there exists no flat timelike rotational surface of parabolic type in E-1(4) with pointwise 1-type Gauss map.
  • Küçük Resim
    Yayın
    Classification of surfaces in a pseudo-sphere with 2-type pseudo-spherical Gauss map
    (Wiley-V C H Verlag GMBH, 2017-11) Bektaş, Burcu; Canfes, Elif Özkara; Dursun, Uğur
    In this article, we study submanifolds in a pseudo-sphere with 2-type pseudo-spherical Gauss map. We give a characterization theorem for Lorentzian surfaces in the pseudosphere S-2(4) subset of E-2(5) with zero mean curvature vector in S-2(4) and 2-type pseudo-spherical Gauss map. We also prove that non-totally umbilical proper pseudo-Riemannian hypersurfaces in a pseudo-sphere S-s(n+1) subset of E-s(n+2) with non-zero constant mean curvature has 2-type pseudo-spherical Gauss map if and only if it has constant scalar curvature. Then, for n = 2 we obtain the classification of surfaces in S-1(3) subset of E-1(4) with 2-type pseudo-spherical Gauss map. Finally, we give an example of surface with null 2-type pseudo-spherical Gauss map which does not appear in Riemannian case, andwe give a characterization theorem for Lorentzian surfaces in S-1(3) subset of E-1(4) with null 2-type pseudospherical Gauss map.
  • Küçük Resim
    Yayın
    Spacelike rotational surfaces of elliptic, hyperbolic and parabolic types in Minkowski Space E-1(4) with pointwise 1-Type Gauss map
    (Springer, 2014-06) Dursun, Uğur; Bektaş, Burcu
    In this paper, we consider a class of spacelike rotational surfaces in Minkowski space E-1(4) with 2-dimensional axis. There are three types of rotational surfaces with 2-dimensional axis, called rotational surfaces of elliptic, hyperbolic or parabolic type. We obtain all flat spacelike rotational surfaces of elliptic and hyperbolic types with pointwise 1-type Gauss map. We also determine flat spacelike rotational surface of parabolic type with pointwise 1-type Gauss map of the first kind. Then, we conclude that there exists no flat spacelike rotational surface of parabolic type in E-1(4) with pointwise 1-type Gauss map of the second kind.
  • Küçük Resim
    Yayın
    On spherical submanifolds with finite type spherical Gauss map
    (Walter De Gruyter GMBH, 2016-04-01) Bektaş, Burcu; Dursun, Uğur
    Chen and Lue (2007) initiated the study of spherical submanifolds with finite type spherical Gauss map. In this paper, we firstly prove that a submanifold Mn of the unit sphere double-struck Sm-1 has non-mass-symmetric 1-type spherical Gauss map if and only if Mn is an open part of a small n-sphere of a totally geodesic (n + 1)-sphere double-struck Sn+1 ? double-struck Sm-1. Then we show that a non-totally umbilical hypersurface M of double-struck Sn+1 with nonzero constant mean curvature in double-struck Sn+1 has mass-symmetric 2-type spherical Gauss map if and only if the scalar curvature curvature of M is constant. Finally, we classify constant mean curvature surfaces in double-struck S3 with mass-symmetric 2-type spherical Gauss map.
  • Küçük Resim
    Yayın
    On pseudo-umbilical rotational surfaces with pointwise 1-type gauss map in E-2(4)
    (Istanbul Technical Univ, 2017-01-01) Bektaş, Burcu; Canfes, Elif Özkara; Dursun, Uğur
    In this work, we study two families of rotational surfaces in the pseudo Euclidean space 1E4 with profile curves lying in 2 dimensional planes. First, we obtain a classification of pseudo umbilical spacelike surfaces and timelike surfaces in these families. Then, we show that in this classification there exists no a pseudo umbilical rotational surface in 1E4 with pointwise 1 type Gauss map of second kind. Finally, we determine such pseudo umbilical rotational surfaces in 1E4 having pointwise 1 type Gauss map of first kind.