In this paper we prove Chen inequalities for submanifolds of real space forms endowed with a semi-symmetric metric connection, i.e., relations between the mean curvature associated with the semi-symmetric metric connection, scalar and sectional curvatures, Ricci curvatures and the sectional curvature of the ambient space. The equality cases are considered.
In this paper, we study the behaviour of submanifolds in statistical
manifolds of constant curvature. We investigate curvature properties of such
submanifolds. Some inequalities for submanifolds with any codimension and
hypersurfaces of statistical manifolds of constant curvature are also
established.
In this paper, we derive an explicit formula for the determinant of Allen's matrix of quasi-sum production functions. We completely classify the quasi-sum production functions by using their Allen determinants. Further, we give some geometric applications of Allen determinants.
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