New examples of CR submanifolds for the 2-jet determination problem

2025/06/26 by Bertrand, Florian, Kolář, Martin, Meylan, Francine
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.21221

Abstract

This paper addresses two questions related to mapping problems. In the first part of the paper, we discuss some recent results regarding the 2-jet determination for biholomorphisms between smooth (weakly) pseudoconvex hypersurfaces; in light of those, we formulate a general problem and illustrate it with examples. In the second part of the paper, we provide a new example of a real submanifold of codimension 7 in ℂ¹⁰ that is not strictly pseudoconvex and for which its germs of CR automorphisms are determined by their 2-jets at a given point.

Citations

• Models of CR Manifolds and Their Symmetry Algebras
• Characterization of real-analytic infinitesimal CR automorphisms for a class of hypersurfaces in \Bbb C⁴.
• The 1-jet determination of stationary discs attached to generic CR submanifolds
• Explicit construction of stationary discs and its consequences for nondegenerate quadrics
• A Counterexample to the 2-jet determination Chern-Moser Theorem in higher codimension
• Nondefective stationary discs and 2-jet determination in higher\n codimension
• Stationary discs and finite jet determination for CR mappings in higher\n codimension
• Stationary discs and finite jet determination for non-degenerate generic\n real submanifolds
• Chern-Moser operators and weighted jet determination problems in higher codimension
• Higher order symmetries of real hypersurfaces in \Bbb C³.
• Stationary holomorphic discs and finite jet determination problems
• Finite jet determination of local analytic CR automorphisms and their parametrization by 2-jets in the finite type case

Related

• Finite jet determination of local analytic CR automorphisms and their parametrization by 2-jets in the finite type case
• A Counterexample to the 2-jet determination Chern-Moser Theorem in higher codimension
• Stationary discs and finite jet determination for CR mappings in higher\n codimension
• Jet determination of smooth CR automorphisms and generalized stationary discs
• Finite jet determination of holomorphic mappings at the boundary