scholarly journals Chen Inequalities for Submanifolds of Real Space Forms with a Ricci Quarter-Symmetric Metric Connection

2019 ◽  
Vol 12 (1) ◽  
pp. 102-110
Author(s):  
Nergiz (önen) POYRAZ ◽  
Halil İbrahim YOLDAŞ
Keyword(s):  
Real Space ◽  
Space Forms ◽  
Real Space Forms ◽  
Metric Connection

scholarly journals Affine connections of non-integrable distributions

2020 ◽  
Vol 17 (08) ◽  
pp. 2050127
Author(s):  
Yong Wang
Keyword(s):  
Riemannian Manifold ◽  
Scalar Curvature ◽  
Constant Scalar Curvature ◽  
Real Space ◽  
Space Forms ◽  
Affine Connections ◽  
Real Space Forms ◽  
Metric Connection ◽  
Statistical Connection

In this paper, we study non-integrable distributions in a Riemannian manifold with a semi-symmetric metric connection, a kind of semi-symmetric non-metric connection and a statistical connection. We obtain the Gauss, Codazzi, and Ricci equations for non-integrable distributions with respect to the semi-symmetric metric connection, the semi-symmetric non-metric connection and the statistical connection. As applications, we obtain Chen’s inequalities for non-integrable distributions of real space forms endowed with a semi-symmetric metric connection and a kind of semi-symmetric non-metric connection. We give some examples of non-integrable distributions in a Riemannian manifold with affine connections. We find some new examples of Einstein distributions and distributions with constant scalar curvature.

Chen Inequalities for Submanifolds of Real Space Forms with a Semi-Symmetric Non-Metric Connection

2012 ◽  
Vol 55 (3) ◽  
pp. 611-622 ◽  
Author(s):  
Cihan Özgür ◽  
Adela Mihai
Keyword(s):  
Sectional Curvature ◽  
Mean Curvature ◽  
Real Space ◽  
Ambient Space ◽  
Space Forms ◽  
Real Space Forms ◽  
Metric Connection ◽  
Sectional Curvatures ◽  
The Mean

AbstractIn this paper we prove Chen inequalities for submanifolds of real space forms endowed with a semi-symmetric non-metric connection, i.e., relations between the mean curvature associated with a semi-symmetric non-metric connection, scalar and sectional curvatures, Ricci curvatures and the sectional curvature of the ambient space. The equality cases are considered.

scholarly journals A Class of Special Hypersurfaces in Real Space Forms

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Yan Zhao ◽  
Ximin Liu
Keyword(s):  
Real Space ◽  
Principal Curvatures ◽  
Space Forms ◽  
Isoparametric Hypersurfaces ◽  
Real Space Forms ◽  
Constant Principal Curvatures

We define the generalized golden- and product-shaped hypersurfaces in real space forms. A hypersurfaceMin real space formsRn+1,Sn+1, andHn+1is isoparametric if it has constant principal curvatures. Based on the classification of isoparametric hypersurfaces, we obtain the whole families of the generalized golden- and product-shaped hypersurfaces in real space forms.

scholarly journals A new characterization of complete linear Weingarten hypersurfaces in real space forms

2013 ◽  
Vol 261 (1) ◽  
pp. 33-43 ◽  
Author(s):  
Cícero Aquino ◽  
Henrique de Lima ◽  
Marco Velásquez
Keyword(s):  
Real Space ◽  
Space Forms ◽  
Linear Weingarten Hypersurfaces ◽  
Real Space Forms
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