scholarly journals Classification of product shaped hypersurfaces in Lorentz space forms

2017 ◽  
Vol 101 (115) ◽  
pp. 223-230
Author(s):  
Dan Yang ◽  
Hao Le ◽  
Bingren Chen
Keyword(s):  
Lorentz Space ◽  
Shape Operator ◽  
Product Type ◽  
De Sitter ◽  
Space Forms ◽  
Isoparametric Hypersurfaces

We define the product shaped hypersurfaces in Lorentz space forms by imposing the shape operator to be product type. Based on the classification of the isoparametric hypersurfaces, we obtain the whole families of the product shaped hypersurfaces in Minkowski, de Sitter and anti-de Sitter spaces.

GOLDEN- AND PRODUCT-SHAPED HYPERSURFACES IN REAL SPACE FORMS

2013 ◽  
Vol 10 (04) ◽  
pp. 1320006 ◽  
Author(s):  
MIRCEA CRASMAREANU ◽  
CRISTINA-ELENA HREŢCANU ◽  
MARIAN-IOAN MUNTEANU
Keyword(s):  
Hyperbolic Space ◽  
Space Form ◽  
Shape Operator ◽  
Real Space ◽  
Clifford Torus ◽  
Space Forms ◽  
Isoparametric Hypersurfaces ◽  
Real Space Forms ◽  
Unit Hypersphere

We define two classes of hypersurfaces in real space forms, golden- and product-shaped, respectively, by imposing the shape operator to be of golden or product type. We obtain the whole families of above hypersurfaces, based on the classification of isoparametric hypersurfaces, as follows: in the golden case all are hyperspheres, a hyperbolic space and a generalized Clifford torus, while for the product case we obtain the unit hypersphere, the hyperplane, a hypersphere and its associated Clifford torus, respectively, according to the type of the ambient space form namely parabolic, hyperbolic or elliptic, respectively.

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.

Classification of the Blaschke Isoparametric Hypersurfaces in Lorentzian Space Forms

2015 ◽  
Vol 65 (3) ◽  
Author(s):  
Fengyun Zhang ◽  
Huafei Sun
Keyword(s):  
Conformal Transformation ◽  
Transformation Group ◽  
Second Fundamental Form ◽  
Conformal Metric ◽  
Space Forms ◽  
Isoparametric Hypersurfaces ◽  
Lorentzian Space ◽  
Blaschke Tensor ◽  
Lorentzian Space Forms

AbstractIn this paper, we study regular immersed hypersurfaces in Lorentzian space forms with a conformal metric, a conformal second fundamental form, the conformal Blaschke tensor and a conformal form, which are invariants under the conformal transformation group. We classify all the immersed hypersurfaces in Lorentzian space forms with two distinct constant Blaschke eigenvalues and vanishing conformal form.

scholarly journals Existence and uniqueness of inhomogeneous ruled hypersurfaces with shape operator of constant norm in the complex hyperbolic space

2021 ◽  
pp. 2150049
Author(s):  
Miguel Domínguez-Vázquez ◽  
Olga Pérez-Barral
Keyword(s):  
Hyperbolic Space ◽  
Complex Space ◽  
Shape Operator ◽  
Complex Hyperbolic Space ◽  
Real Hypersurfaces ◽  
Space Forms ◽  
Nonflat Complex Space Forms ◽  
Ruled Real Hypersurfaces ◽  
Complex Space Forms

We complete the classification of ruled real hypersurfaces with shape operator of constant norm in nonflat complex space forms by showing the existence of a unique inhomogeneous example in the complex hyperbolic space.

scholarly journals A classification of Riemannian 3-manifolds with constant principal ricci curvaturesρ1= ρ2≠ ρ3

1993 ◽  
Vol 132 ◽  
pp. 1-36 ◽  
Author(s):  
Oldřich Kowalski
Keyword(s):  
Differential Geometry ◽  
Homogeneous Spaces ◽  
Space Forms ◽  
Isoparametric Hypersurfaces ◽  
Main Motivation ◽  
Locally Homogeneous ◽  
Riemannian Spaces

This paper has been motivated by various problems and results in differential geometry. The main motivation is the study of curvature homogeneous Riemannian spaces initiated in 1960 by I.M. Singer (see Section 9—Appendix for the precise definitions and references). Up to recently, only sporadic classes of examples have been known of curvature homogeneous spaces which are not locally homogeneous. For instance, isoparametric hypersurfaces in space forms give nice examples of nontrivial curvature homogeneous spaces (see [FKM]). To study the topography of curvature homogeneous spaces more systematically, it is natural to start with the dimension n = 3. The following results and problems have been particularly inspiring.

scholarly journals Classification of f-biharmonic submanifolds in Lorentz space forms

2021 ◽  
Vol 19 (1) ◽  
pp. 1299-1314
Author(s):  
Li Du
Keyword(s):  
Vector Field ◽  
Mean Curvature ◽  
Lorentz Space ◽  
Curvature Vector ◽  
Shape Operator ◽  
Mean Curvature Vector ◽  
Biharmonic Submanifolds ◽  
Parallel Mean Curvature Vector ◽  
Space Forms ◽  
Parallel Mean Curvature

Abstract In this paper, f-biharmonic submanifolds with parallel normalized mean curvature vector field in Lorentz space forms are discussed. When f f is a constant, we prove that such submanifolds have parallel mean curvature vector field with the minimal polynomial of the shape operator of degree ≤ 2 \le 2 . When f f is a function, we completely classify such pseudo-umbilical submanifolds.

scholarly journals On a solvable class of product-type systems of difference equations

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6113-6129 ◽  
Author(s):  
Stevo Stevic ◽  
Bratislav Iricanin ◽  
Zdenk Smarda
Keyword(s):  
Closed Form ◽  
Difference Equations ◽  
Type Systems ◽  
Product Type ◽  
Dependent Variables ◽  
Solvable Class ◽  
Solvable Product

It is shown that the following class of systems of difference equations zn+1 = ?zanwbn, wn+1 = ?wcnzdn-2, n ? N0, where a,b,c,d ? Z, ?, ?, z-2, z-1, z0,w0 ? C \ {0}, is solvable, continuing our investigation of classification of solvable product-type systems with two dependent variables. We present closed form formulas for solutions to the systems in all the cases. In the main case, when bd ? 0, a detailed investigation of the form of the solutions is presented in terms of the zeros of an associated polynomial whose coefficients depend on some of the parameters of the system.

Sign in / Sign up

Export Citation Format

Share Document