CR rigidity of pseudo harmonic maps and pseudo biharmonic maps
Hajime Urakawa
TL;DR
This paper explores the properties of pseudo biharmonic and pseudo harmonic maps in CR geometry, characterizing certain immersions and providing examples, thus advancing understanding of CR analogue conjectures.
Contribution
It introduces the CR analogue of B.-Y. Chen's conjecture and characterizes pseudo biharmonic isometric immersions with parallel pseudo mean curvature.
Findings
Pseudo biharmonic but not pseudo harmonic isometric immersions characterized.
Several examples of pseudo biharmonic maps provided.
CR analogue of Chen's conjecture discussed.
Abstract
The CR analogue of B.-Y. Chen's conjecture on pseudo biharmonic maps will be shown. Pseudo biharmonic, but not pseudo harmonic, isometric immersions with parallel pseudo mean curvature vector fields, will be characterized. Several examples of pseudo biharmonic maps will be given.
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Taxonomy
TopicsHolomorphic and Operator Theory · Analytic and geometric function theory · Geometric Analysis and Curvature Flows