Chen inequalities on lightlike hypersurfaces of a GRW spacetime

In this paper, we introduce [Formula: see text]-Ricci curvature and [Formula: see text]-scalar curvature on lightlike hypersurfaces of a GRW spacetime. Using these curvatures, we establish some inequalities for lightlike hypersurfaces of a GRW spacetime. Using these inequalities, we obtain some characterizations on lightlike hypersurfaces. We also get Chen–Ricci inequality and Chen inequality on a screen homothetic lightlike hypersurfaces of a GRW spacetime.

Relations between Extrinsic and Intrinsic Invariants of Statistical Submanifolds in Sasaki-Like Statistical Manifolds

The Chen first inequality and a Chen inequality for the δ(2,2)-invariant on statistical submanifolds of Sasaki-like statistical manifolds, under a curvature condition, are obtained.

A New Algebraic Inequality and Some Applications in Submanifold Theory

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.

An Algebraic Inequality with Applications to Certain Chen Inequalities

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

Geometry of Chen invariants in statistical warped product manifolds

In this paper, we derive Chen inequality for statistical submanifold of statistical warped product manifolds [Formula: see text]. Further, we derive Chen inequality for Legendrian statistical submanifold in statistical warped product manifolds [Formula: see text]. We also provide some applications of derived inequalities in a statistical warped product manifold which is equivalent to a hyperbolic space. Moreover, we construct new examples of statistical warped product manifolds to support results.

The δ(2,2)-Invariant on Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature

We establish Chen inequality for the invariant δ ( 2 , 2 ) on statistical submanifolds in Hessian manifolds of constant Hessian curvature. Recently, in co-operation with Chen, we proved a Chen first inequality for such submanifolds. The present authors previously initiated the investigation of statistical submanifolds in Hessian manifolds of constant Hessian curvature; this paper represents a development in this topic.

Chen Inequalities for Statistical Submanifolds of Kähler-Like Statistical Manifolds

We consider Kähler-like statistical manifolds, whose curvature tensor field satisfies a natural condition. For their statistical submanifolds, we prove a Chen first inequality and a Chen inequality for the invariant δ ( 2 , 2 ) .

Submanifolds in Normal Complex Contact Manifolds

In the present article we initiate the study of submanifolds in normal complex contact metric manifolds. We define invariant and anti-invariant ( C C -totally real) submanifolds in such manifolds and start the study of their basic properties. Also, we establish the Chen first inequality and Chen inequality for the invariant δ ( 2 , 2 ) for C C -totally real submanifolds in a normal complex contact space form and characterize the equality cases. We also prove the minimality of C C -totally real submanifolds of maximum dimension satisfying the equalities.

Some inequalities for statistical submanifolds of quaternion Kaehler-like statistical space forms

Motivated by one of the problems proposed by [Vilcu and Vilcu, Statistical manifolds with almost quaternionic structures and quaternionic Kaehler-like statistical submersions, Entropy 17 (2015) 6213–6228] in this paper, we study the statistical submanifolds of quaternion Kaehler-like statistical space forms and provide an answer to the problem. Further, we derive the statistical version of Chen inequality for totally real statistical submanifold in such ambient.