A Characterization of Ruled Real Hypersurfaces in Non-Flat Complex Space Forms
The Levi-Civita connection and the k-th generalized Tanaka-Webster connection are defined on a real hypersurface <i>M</i> in a non-flat complex space form. For any nonnull constant <i>k</i> and any vector field <i>X</i> tangent to <i>M</i> the k-th Cho...
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doaj-69e26b4cc0544bf89dde939a453d2a372020-11-25T02:03:02ZengMDPI AGMathematics2227-73902020-04-01864264210.3390/math8040642A Characterization of Ruled Real Hypersurfaces in Non-Flat Complex Space FormsGeorge Kaimakamis0Konstantina Panagiotidou1Juan de Dios Pérez2Faculty of Mathematics and Engineering Sciences, Hellenic Army Academy, Vari, 16673 Attiki, GreeceFaculty of Mathematics and Engineering Sciences, Hellenic Army Academy, Vari, 16673 Attiki, GreeceDepartmento de Geometria y Topologia, Universidad de Granada, 18071 Granada, SpainThe Levi-Civita connection and the k-th generalized Tanaka-Webster connection are defined on a real hypersurface <i>M</i> in a non-flat complex space form. For any nonnull constant <i>k</i> and any vector field <i>X</i> tangent to <i>M</i> the k-th Cho operator <inline-formula> <math display="inline"> <semantics> <msubsup> <mi>F</mi> <mi>X</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> </semantics> </math> </inline-formula> is defined and is related to both connections. If <i>X</i> belongs to the maximal holomorphic distribution <inline-formula> <math display="inline"> <semantics> <mi mathvariant="double-struck">D</mi> </semantics> </math> </inline-formula> on <i>M</i>, the corresponding operator does not depend on <i>k</i> and is denoted by <inline-formula> <math display="inline"> <semantics> <msub> <mi>F</mi> <mi>X</mi> </msub> </semantics> </math> </inline-formula> and called Cho operator. In this paper, real hypersurfaces in non-flat space forms such that <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>F</mi> <mi>X</mi> </msub> <mi>S</mi> <mo>=</mo> <mi>S</mi> <msub> <mi>F</mi> <mi>X</mi> </msub> </mrow> </semantics> </math> </inline-formula>, where <i>S</i> denotes the Ricci tensor of <i>M</i> and a further condition is satisfied, are classified.https://www.mdpi.com/2227-7390/8/4/642k-th generalized Tanaka-Webster connectionk-th Cho operatorreal hypersurfaceRicci tensornon-flat complex space form |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
George Kaimakamis Konstantina Panagiotidou Juan de Dios Pérez |
spellingShingle |
George Kaimakamis Konstantina Panagiotidou Juan de Dios Pérez A Characterization of Ruled Real Hypersurfaces in Non-Flat Complex Space Forms Mathematics k-th generalized Tanaka-Webster connection k-th Cho operator real hypersurface Ricci tensor non-flat complex space form |
author_facet |
George Kaimakamis Konstantina Panagiotidou Juan de Dios Pérez |
author_sort |
George Kaimakamis |
title |
A Characterization of Ruled Real Hypersurfaces in Non-Flat Complex Space Forms |
title_short |
A Characterization of Ruled Real Hypersurfaces in Non-Flat Complex Space Forms |
title_full |
A Characterization of Ruled Real Hypersurfaces in Non-Flat Complex Space Forms |
title_fullStr |
A Characterization of Ruled Real Hypersurfaces in Non-Flat Complex Space Forms |
title_full_unstemmed |
A Characterization of Ruled Real Hypersurfaces in Non-Flat Complex Space Forms |
title_sort |
characterization of ruled real hypersurfaces in non-flat complex space forms |
publisher |
MDPI AG |
series |
Mathematics |
issn |
2227-7390 |
publishDate |
2020-04-01 |
description |
The Levi-Civita connection and the k-th generalized Tanaka-Webster connection are defined on a real hypersurface <i>M</i> in a non-flat complex space form. For any nonnull constant <i>k</i> and any vector field <i>X</i> tangent to <i>M</i> the k-th Cho operator <inline-formula> <math display="inline"> <semantics> <msubsup> <mi>F</mi> <mi>X</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> </semantics> </math> </inline-formula> is defined and is related to both connections. If <i>X</i> belongs to the maximal holomorphic distribution <inline-formula> <math display="inline"> <semantics> <mi mathvariant="double-struck">D</mi> </semantics> </math> </inline-formula> on <i>M</i>, the corresponding operator does not depend on <i>k</i> and is denoted by <inline-formula> <math display="inline"> <semantics> <msub> <mi>F</mi> <mi>X</mi> </msub> </semantics> </math> </inline-formula> and called Cho operator. In this paper, real hypersurfaces in non-flat space forms such that <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>F</mi> <mi>X</mi> </msub> <mi>S</mi> <mo>=</mo> <mi>S</mi> <msub> <mi>F</mi> <mi>X</mi> </msub> </mrow> </semantics> </math> </inline-formula>, where <i>S</i> denotes the Ricci tensor of <i>M</i> and a further condition is satisfied, are classified. |
topic |
k-th generalized Tanaka-Webster connection k-th Cho operator real hypersurface Ricci tensor non-flat complex space form |
url |
https://www.mdpi.com/2227-7390/8/4/642 |
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