TY - JOUR
T1 - Pseudo-Spherical Submanifolds with 1-Type Pseudo-Spherical Gauss Map
AU - Bektaş, Burcu
AU - Canfes, Elif Özkara
AU - Dursun, Uğur
N1 - Publisher Copyright:
© 2016, Springer International Publishing.
PY - 2017/6/1
Y1 - 2017/6/1
N2 - 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 Ss4(1) with index s, s= 1 , 2 , and having harmonic pseudo-spherical Gauss map. Then we give a characterization theorem for pseudo-Riemannian submanifolds of a pseudo-sphere Ssm-1(1)⊂Esm with 1-type pseudo-spherical Gauss map, and we classify spacelike surfaces and Lorentzian surfaces in the de Sitter space S14(1)⊂E15 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.
AB - 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 Ss4(1) with index s, s= 1 , 2 , and having harmonic pseudo-spherical Gauss map. Then we give a characterization theorem for pseudo-Riemannian submanifolds of a pseudo-sphere Ssm-1(1)⊂Esm with 1-type pseudo-spherical Gauss map, and we classify spacelike surfaces and Lorentzian surfaces in the de Sitter space S14(1)⊂E15 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.
KW - Finite type mapping
KW - biharmonic Gauss map
KW - marginally trapped surface
KW - pseudo-sphere
KW - pseudo-spherical Gauss map
UR - http://www.scopus.com/inward/record.url?scp=84970997344&partnerID=8YFLogxK
U2 - 10.1007/s00025-016-0560-9
DO - 10.1007/s00025-016-0560-9
M3 - Article
AN - SCOPUS:84970997344
SN - 1422-6383
VL - 71
SP - 867
EP - 887
JO - Results in Mathematics
JF - Results in Mathematics
IS - 3-4
ER -