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

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 $$\mathbb {C}^{10}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mn>10</mml:mn> </mml:msup> </mml:math> that is not strictly pseudoconvex and for which its germs of CR automorphisms are determined by their 2-jets at a given point.