On CR Submanifolds of Maximal CR Dimension with Flat Normal Connection of a Complex Projective Space
Liang Zhang, Man Su, Pan Zhang
TL;DR
This paper investigates CR submanifolds with maximal CR dimension and flat normal connection in complex projective spaces, proving the non-existence of certain classes and analyzing umbilical normal vectors.
Contribution
It provides new results on the non-existence of specific CR submanifolds with flat normal connection and analyzes the position of umbilical normal vectors, especially in dimension 3.
Findings
Non-existence of certain CR submanifolds with flat normal connection
Characterization of umbilical normal vectors in dimension 3
Insights into the geometry of CR submanifolds in complex projective spaces
Abstract
In this paper, we study the CR submanifolds of maximal CR dimension with flat normal connection of a complex projective space. We first investigate the position of the umbilical normal vector in the normal bundle, especially for the submanifolds of dimension 3. Then as the application, we prove the non-existence of a class of CR submanifolds of maximal CR dimension with flat normal connection.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Holomorphic and Operator Theory · Point processes and geometric inequalities