A Chen first inequality for statistical submanifolds in Hessian manifolds of constant Hessian curvature
… Chen introduced a new type of curvature invariants, known as Chen invariants (cf. [7, 8]
for details). This study of Chen invariants was started in [4], where he proved the Chen first
inequality for submanifolds in Riemannian space forms. Recall that the Chen first invariant
of a Riemannian manifold \(M^n\) is defined by \(\delta _{M^n}=\tau -\inf K\), where \(\tau \)
and K are the scalar and sectional curvatures of \(M^n\), respectively. …
for details). This study of Chen invariants was started in [4], where he proved the Chen first
inequality for submanifolds in Riemannian space forms. Recall that the Chen first invariant
of a Riemannian manifold \(M^n\) is defined by \(\delta _{M^n}=\tau -\inf K\), where \(\tau \)
and K are the scalar and sectional curvatures of \(M^n\), respectively. …
Abstract
The study of statistical submanifolds in Hessian manifolds of constant Hessian curvature was started by two of the present authors. We continue this work and establish a Chen first inequality for such submanifolds.
Springer
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