On CR-statistical submanifolds of holomorphic statistical manifolds
Aliya Naaz Sıddıquı, Falleh R. Al‐Solamy, Mohammad Hasan Shahid, Ion Mihaid
Abstract
In the present paper, weinvestigate some properties of the distributions involved in the definition of a CR-statistical submanifold. The characterization of a CR-product in holomorphic statistical manifolds is given. By using an optimization technique, we establish a relationship between the Ricci curvature and the squared norm of the mean curvature of any submanifold in the same ambient space. The equality case is also discussed here. This paper finishes with some related examples.
Topics & Concepts
MathematicsSubmanifoldHolomorphic functionPure mathematicsNorm (philosophy)CurvatureRicci curvatureMean curvatureMathematical analysisSectional curvatureCharacterization (materials science)Product (mathematics)Scalar curvatureGeometryLawPolitical scienceNanotechnologyMaterials sciencePoint processes and geometric inequalitiesGeometric Analysis and Curvature Flows