ISOTROPIC IMMERSIONS OF RANK ONE SYMMETRIC SPACES INTO REAL SPACE FORMS AND MEAN CURVATURES

2005 ◽  
Author(s):  
NOBUTAKA BOUMUKI
Keyword(s):  
Symmetric Spaces ◽  
Real Space ◽  
Space Forms ◽  
Real Space Forms ◽  
Rank One

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

scholarly journals The floating body in real space forms

2018 ◽  
Vol 110 (2) ◽  
pp. 187-220 ◽  
Author(s):  
Florian Besau ◽  
Elisabeth M. Werner
Keyword(s):  
Real Space ◽  
Floating Body ◽  
Space Forms ◽  
Real Space Forms

Isotropic Immersions with Low Codimension of Complex Space Forms into Real Space Forms

2004 ◽  
Vol 47 (4) ◽  
pp. 492-503
Author(s):  
Nobutaka Boumuki
Keyword(s):  
Complex Space ◽  
Real Space ◽  
Space Forms ◽  
Real Space Forms ◽  
Complex Space Forms

AbstractThe main purpose of this paper is to determine isotropic immersions of complex space forms into real space forms with low codimension. This is an improvement of a result of S. Maeda.

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