Blow-ups and infinitesimal automorphisms of CR-manifolds
Blow-ups and infinitesimal automorphisms of CR-manifolds
Abstract For a real-analytic connected CR-hypersurface M of CR-dimension $$n\geqslant 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>n</mml:mi><mml:mo>⩾</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> having a point of Levi-nondegeneracy the following alternative is demonstrated for its symmetry algebra $$\mathfrak {s}={\mathfrak {s}}(M)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>s</mml:mi><mml:mo>=</mml:mo><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>M</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> : (i) either $$\dim {\mathfrak {s}}=n^2+4n+3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>dim</mml:mo><mml:mi>s</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mi>n</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:mn>4</mml:mn><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math> and M is spherical everywhere; (ii) or $$\dim {\mathfrak {s}}\leqslant …