A Classification of Three-dimensional Real Hypersurfaces in Non-flat Complex Space Forms in Terms of their Generalized Tanaka–Webster Lie Derivative
Canadian mathematical bulletin, Tome 59 (2016) no. 4, pp. 813-823
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On a real hypersurface $M$ in a non-flat complex space form there exist the Levi–Civita and the $k$ -th generalized Tanaka–Webster connections. The aim of this paper is to study three dimensional real hypersurfaces in non-flat complex space forms, whose Lie derivative of the structure Jacobi operatorwith respect to the Levi–Civita connection coincides with the Lie derivative of it with respect to the $k$ -th generalized Tanaka-Webster connection. The Lie derivatives are considered in direction of the structure vector field and in direction of any vector field orthogonal to the structure vector field.
Mots-clés :
53C15, 53B25, k-th generalized Tanaka–Webster connection, non-flat complex space form, real hypersurface, Lie derivative, structure Jacobi operator
Kaimakamis, George; Panagiotidou, Konstantina; Perez, Juan de Dios. A Classification of Three-dimensional Real Hypersurfaces in Non-flat Complex Space Forms in Terms of their Generalized Tanaka–Webster Lie Derivative. Canadian mathematical bulletin, Tome 59 (2016) no. 4, pp. 813-823. doi: 10.4153/CMB-2016-042-2
@article{10_4153_CMB_2016_042_2,
author = {Kaimakamis, George and Panagiotidou, Konstantina and Perez, Juan de Dios},
title = {A {Classification} of {Three-dimensional} {Real} {Hypersurfaces} in {Non-flat} {Complex} {Space} {Forms} in {Terms} of their {Generalized} {Tanaka{\textendash}Webster} {Lie} {Derivative}},
journal = {Canadian mathematical bulletin},
pages = {813--823},
year = {2016},
volume = {59},
number = {4},
doi = {10.4153/CMB-2016-042-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-042-2/}
}
TY - JOUR AU - Kaimakamis, George AU - Panagiotidou, Konstantina AU - Perez, Juan de Dios TI - A Classification of Three-dimensional Real Hypersurfaces in Non-flat Complex Space Forms in Terms of their Generalized Tanaka–Webster Lie Derivative JO - Canadian mathematical bulletin PY - 2016 SP - 813 EP - 823 VL - 59 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-042-2/ DO - 10.4153/CMB-2016-042-2 ID - 10_4153_CMB_2016_042_2 ER -
%0 Journal Article %A Kaimakamis, George %A Panagiotidou, Konstantina %A Perez, Juan de Dios %T A Classification of Three-dimensional Real Hypersurfaces in Non-flat Complex Space Forms in Terms of their Generalized Tanaka–Webster Lie Derivative %J Canadian mathematical bulletin %D 2016 %P 813-823 %V 59 %N 4 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-042-2/ %R 10.4153/CMB-2016-042-2 %F 10_4153_CMB_2016_042_2
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