scholarly journals A New Algebraic Inequality and Some Applications in Submanifold Theory

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1175
Author(s):  
Ion Mihai ◽  
Radu-Ioan Mihai
Keyword(s):  
Simple Proof ◽  
Riemannian Space ◽  
Space Forms ◽  
Riemannian Space Forms ◽  
Chen Inequality

We give a simple proof of the Chen inequality involving the Chen invariant δ(k) of submanifolds in Riemannian space forms. We derive Chen’s first inequality and the Chen–Ricci inequality. Additionally, we establish a corresponding inequality for statistical submanifolds.

scholarly journals An Algebraic Inequality with Applications to Certain Chen Inequalities

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 7
Author(s):  
Ion Mihai ◽  
Radu-Ioan Mihai
Keyword(s):  
Simple Proof ◽  
Riemannian Space ◽  
Space Forms ◽  
Riemannian Space Forms ◽  
Chen Inequality

We give a simple proof of the Chen inequality for the Chen invariant δ(2,⋯,2)︸kterms of submanifolds in Riemannian space forms.

scholarly journals Uniqueness of Curvature Measures in Pseudo-Riemannian Geometry

2021 ◽  
Author(s):  
Andreas Bernig ◽  
Dmitry Faifman ◽  
Gil Solanes
Keyword(s):  
Riemannian Manifolds ◽  
Riemannian Geometry ◽  
Riemannian Space ◽  
Space Forms ◽  
Type Formula ◽  
Isometric Embeddings ◽  
Curvature Measures ◽  
Riemannian Space Forms

AbstractThe recently introduced Lipschitz–Killing curvature measures on pseudo-Riemannian manifolds satisfy a Weyl principle, i.e. are invariant under isometric embeddings. We show that they are uniquely characterized by this property. We apply this characterization to prove a Künneth-type formula for Lipschitz–Killing curvature measures, and to classify the invariant generalized valuations and curvature measures on all isotropic pseudo-Riemannian space forms.

scholarly journals On some generalized Einstein metric conditions on hypersurfaces in semi-Riemannian space forms

2003 ◽  
Vol 96 (2) ◽  
pp. 149-166 ◽  
Author(s):  
Ryszard Deszcz ◽  
Małgorzata Głogowska ◽  
Marian Hotloś ◽  
Leopold Verstraelen
Keyword(s):  
Riemannian Space ◽  
Einstein Metric ◽  
Space Forms ◽  
Riemannian Space Forms

scholarly journals B.-Y. Chen inequalities for semislant submanifolds in Sasakian space forms

2003 ◽  
Vol 2003 (27) ◽  
pp. 1731-1738 ◽  
Author(s):  
Dragoş Cioroboiu
Keyword(s):  
Vector Field ◽  
Mean Curvature ◽  
Riemannian Space ◽  
Sasakian Manifold ◽  
Sharp Inequality ◽  
Space Forms ◽  
Reeb Vector ◽  
Reeb Vector Field ◽  
Sasakian Space Forms ◽  
Riemannian Space Forms

Chen (1993) established a sharp inequality for the sectional curvature of a submanifold in Riemannian space forms in terms of the scalar curvature and squared mean curvature. The notion of a semislant submanifold of a Sasakian manifold was introduced by J. L. Cabrerizo, A. Carriazo, L. M. Fernandez, and M. Fernandez (1999). In the present paper, we establish Chen inequalities for semislant submanifolds in Sasakian space forms by using subspaces orthogonal to the Reeb vector fieldξ.

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