scholarly journals Isoparametric hypersurfaces in Finsler space forms

2021 ◽  
Author(s):  
Qun He ◽  
Yali Chen ◽  
Songting Yin ◽  
Tingting Ren
Keyword(s):  
Finsler Space ◽  
Space Forms ◽  
Isoparametric Hypersurfaces

Classifications of Isoparametric Hypersurfaces in Randers Space Forms

2020 ◽  
Vol 36 (9) ◽  
pp. 1049-1060
Author(s):  
Qun He ◽  
Pei Long Dong ◽  
Song Ting Yin
Keyword(s):  
Space Forms ◽  
Isoparametric Hypersurfaces ◽  
Randers Space

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.

The isoperimetric problem in the 2-dimensional Finsler space forms with k = 0

2019 ◽  
Vol 30 (01) ◽  
pp. 1950005 ◽  
Author(s):  
Linfeng zhou
Keyword(s):  
Space Form ◽  
Finsler Space ◽  
Isoperimetric Problem ◽  
Local Maximum ◽  
Space Forms ◽  
Maximum Area

In this paper, the isoperimetric problem in the 2-dimensional Finsler space form [Formula: see text] with [Formula: see text] by using the Busemann–Hausdorff area is investigated. We prove that the circle centered the origin achieves the local maximum area of the isoperimetric problem.

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.

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 Null hypersurfaces in indefinite nearly Kaehlerian Finsler spaces

2019 ◽  
Author(s):  
Samuel Ssekajja
Keyword(s):  
Vector Fields ◽  
Finsler Space ◽  
Second Fundamental Form ◽  
Finsler Spaces ◽  
Space Forms ◽  
Null Hypersurfaces ◽  
Geometric Conditions ◽  
Cr Structure ◽  
Sectional Curvatures ◽  
New Inequalities

We study the geometry of null hypersurfaces, $M$, in indefinite nearly Kaehlerian Finsler space forms $\mathbb{F}^{2n}$. We prove new inequalities involving the point-wise vertical sectional curvatures of $\mathbb{F}^{2n}$, based on two special vector fields on an umbilic hypersurface. Such inequalities generalize some known results on null hypersurfaces of Kaehlerian space forms. Furthermore, under some geometric conditions, we show that the null hypersurface $(M, B)$, where $B$ is the local second fundamental form of $M$, is locally isometric to the null product $M_{D}\times M_{D'}$, where $M_{D}$ and $M_{D'}$ are the leaves of the distributions $D$ and $D'$ which constitutes the natural null-CR structure on $M$.

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