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On a New type of Tensor on Real Hypersurfaces in Non-Flat Complex Space Forms

Faculty of Mathematics and Engineering Sciences, Hellenic Army Academy, Vari, 16673 Attiki, Greece
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Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Symmetry 2019, 11(4), 559; https://doi.org/10.3390/sym11040559
Received: 17 March 2019 / Revised: 11 April 2019 / Accepted: 16 April 2019 / Published: 18 April 2019
(This article belongs to the Special Issue Geometry of Submanifolds and Homogeneous Spaces)
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Abstract

In this paper the notion of -Weyl curvature tensor on real hypersurfaces in non-flat complex space forms is introduced. It is related to the -Ricci tensor of a real hypersurface. The aim of this paper is to provide two classification theorems concerning real hypersurfaces in non-flat complex space forms in terms of -Weyl curvature tensor. More precisely, Hopf hypersurfaces of dimension greater or equal to three in non-flat complex space forms with vanishing -Weyl curvature tensor are classified. Next, all three dimensional real hypersurfaces in non-flat complex space forms, whose -Weyl curvature tensor vanishes identically are classified. The used methods are based on tools from differential geometry and solving systems of differential equations. View Full-Text
Keywords: real hypersurfaces; non-flat complex space forms; *-Ricci tensor; *-Weyl curvature tensor real hypersurfaces; non-flat complex space forms; *-Ricci tensor; *-Weyl curvature tensor
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Kaimakamis, G.; Panagiotidou, K. On a New type of Tensor on Real Hypersurfaces in Non-Flat Complex Space Forms. Symmetry 2019, 11, 559.

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