scholarly journals Quantitative stability for hypersurfaces with almost constant curvature in space forms

2021 ◽  
Author(s):  
Giulio Ciraolo ◽  
Alberto Roncoroni ◽  
Luigi Vezzoni
Keyword(s):  
Constant Curvature ◽  
Space Forms ◽  
Quantitative Stability

scholarly journals On constant curvature submanifolds of space forms

2021 ◽  
Vol 75 ◽  
pp. 101718
Author(s):  
M. Dajczer ◽  
C.-R. Onti ◽  
Th. Vlachos
Keyword(s):  
Constant Curvature ◽  
Space Forms

scholarly journals CLASSIFICATION OF LAGRANGIAN SURFACES OF CONSTANT CURVATURE IN THE COMPLEX EUCLIDEAN PLANE

2005 ◽  
Vol 48 (2) ◽  
pp. 337-364 ◽  
Author(s):  
Bang-Yen Chen
Keyword(s):  
Constant Curvature ◽  
Euclidean Plane ◽  
Lagrangian Submanifolds ◽  
Real Space ◽  
Point Of View ◽  
Space Forms ◽  
Lagrangian Surfaces ◽  
Real Space Forms ◽  
Geometric Point

AbstractOne of the most fundamental problems in the study of Lagrangian submanifolds from a Riemannian geometric point of view is the classification of Lagrangian immersions of real-space forms into complex-space forms. In this article, we solve this problem for the most basic case; namely, we classify Lagrangian surfaces of constant curvature in the complex Euclidean plane $\mathbb{C}^2$. Our main result states that there exist 19 families of Lagrangian surfaces of constant curvature in $\mathbb{C}^2$. Twelve of the 19 families are obtained via Legendre curves. Conversely, Lagrangian surfaces of constant curvature in $\mathbb{C}^2$ can be obtained locally from the 19 families.

scholarly journals A characterization of minimal ascreen null hypersurfaces of $(LCS)$-space forms

2019 ◽  
Author(s):  
Samuel Ssekajja
Keyword(s):  
Constant Curvature ◽  
Ricci Tensor ◽  
Space Form ◽  
Null Hypersurface ◽  
Space Forms ◽  
Screen Distribution ◽  
Null Hypersurfaces ◽  
Null Curve

In the present paper, we study nontotally geodesic minimal ascreen null hypersurface, $M$, of a Lorentzian concircular structure $(LCS)$-space form of constant curvature $0$ or $1$. We prove that; if the Ricci tensor of $M$ is parallel with respect to any leaf of its screen distribution, then $M$ is isometric to a product of a null curve and spheres.

scholarly journals Pinching Theorems for Statistical Submanifolds in Sasaki-Like Statistical Space Forms

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 690 ◽  
Author(s):  
Ali Alkhaldi ◽  
Mohd. Aquib ◽  
Aliya Siddiqui ◽  
Mohammad Shahid
Keyword(s):  
Constant Curvature ◽  
Necessary And Sufficient Condition ◽  
Einstein Field Equations ◽  
Statistical Manifold ◽  
Field Equations ◽  
Space Forms ◽  
Equality Case ◽  
Statistical Manifolds ◽  
Necessary And Sufficient ◽  
Statistical Space

In this paper, we obtain the upper bounds for the normalized δ -Casorati curvatures and generalized normalized δ -Casorati curvatures for statistical submanifolds in Sasaki-like statistical manifolds with constant curvature. Further, we discuss the equality case of the inequalities. Moreover, we give the necessary and sufficient condition for a Sasaki-like statistical manifold to be η -Einstein. Finally, we provide the condition under which the metric of Sasaki-like statistical manifolds with constant curvature is a solution of vacuum Einstein field equations.

scholarly journals On 3-Dimensional Contact Metric Generalized(k,μ)-Space Forms

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
D. G. Prakasha ◽  
Shyamal Kumar Hui ◽  
Kakasab Mirji
Keyword(s):  
Constant Curvature ◽  
Space Form ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Space Forms ◽  
3 Dimensional ◽  
Projectively Flat ◽  
Necessary And Sufficient

The present paper deals with a study of 3-dimensional contact metric generalized(k,μ)-space forms. We obtained necessary and sufficient condition for a 3-dimensional contact metric generalized(k,μ)-space form withQϕ=ϕQto be of constant curvature. We also obtained some conditions of such space forms to be pseudosymmetric andξ-projectively flat, respectively.

Sign in / Sign up

Export Citation Format

Share Document