scholarly journals Ricci and Casorati principal directions of Wintgen ideal submanifolds

Filomat ◽  
2014 ◽  
Vol 28 (4) ◽  
pp. 657-661 ◽  
Author(s):  
Simona Decu ◽  
Miroslava Petrovic-Torgasev ◽  
Aleksandar Sebekovic ◽  
Leopold Verstraelend
Keyword(s):  
Real Space ◽  
Space Forms ◽  
Real Space Forms ◽  
Principal Directions ◽  
Wintgen Ideal Submanifolds

We show that for Wintgen ideal submanifolds in real space forms the (intrinsic) Ricci principal directions and the (extrinsic) Casorati principal directions coincide.

scholarly journals On the intrinsic Deszcz symmetries and the extrinsic Chen character of Wintgen ideal submanifolds

2010 ◽  
Vol 41 (2) ◽  
pp. 109-116 ◽  
Author(s):  
S. Decu ◽  
M. Petrovic-Torgasev ◽  
A. Sebekovic ◽  
L. Verstraelen
Keyword(s):  
Ricci Curvature ◽  
Curvature Tensor ◽  
Real Space ◽  
Space Forms ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Real Space Forms ◽  
Wintgen Ideal Submanifolds ◽  
Weyl Conformal Curvature Tensor

In this paper it is shown that all Wintgen ideal submanifolds in ambient real space forms are Chen submanifolds. It is also shown that the Wintgen ideal submanifolds of dimension $ >3 $ in real space forms do intrinsically enjoy some curvature symmetries in the sense of Deszcz of their Riemann--Christoffel curvature tensor, of their Ricci curvature tensor and of their Weyl conformal curvature tensor.

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

scholarly journals A fundamental theorem for submanifolds of multiproducts of real space forms

2017 ◽  
Vol 17 (3) ◽  
Author(s):  
Marie-Amélie Lawn ◽  
Julien Roth
Keyword(s):  
Minimal Surfaces ◽  
Fundamental Theorem ◽  
Arbitrary Number ◽  
Real Space ◽  
Isometric Immersions ◽  
Space Forms ◽  
Real Space Forms ◽  
Simply Connected ◽  
Bonnet Theorem

AbstractWe prove a Bonnet theorem for isometric immersions of submanifolds into the products of an arbitrary number of simply connected real space forms. Then we prove the existence of associate families of minimal surfaces in such products. Finally, in the case of 𝕊

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