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NOWHERE MINIMAL CR SUBMANIFOLDS AND LEVI-FLAT HYPERSURFACES

Jiř́í Lebl

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Abstract

A local uniqueness property of holomorphic functions on real-analytic nowhere minimal CR submanifolds of higher codimension is investigated. A sufficient condition called almost minimality is given and studied. A weaker necessary condition, being contained a possibly singular real-analytic Levi-flat hypersurface is studied and characterized. This question is completely resolved for algebraic submanifolds of codimension 2 and a sufficient condition for non containment is given for non algebraic submanifolds. As a consequence, an example of a submanifold ofcodimension 2, not biholomorphically equivalent to an algebraic one, is given. We also investigate the structure ofsingularities of Levi-flat hypersurfaces.

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What this paper is about

A local uniqueness property of holomorphic functions on real-analytic nowhere minimal CR submanifolds of higher codimension is investigated. A sufficient condition called almost minimality is given and studied. A weaker necessary condition, being contained a possibly singular real-analytic Levi-flat hypersurface is studied and characterized. This question is completely resolved for algebraic submanifolds of codimension 2 and a sufficient condition for non containment is given for non algebraic submanifolds. As a consequence, an example of a submanifold ofcodimension 2, not biholomorphically equivalent to an algebraic one, is given. We also investigate the structure ofsingularities of Levi-flat hypersurfaces.

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Available abstract

A local uniqueness property of holomorphic functions on real-analytic nowhere minimal CR submanifolds of higher codimension is investigated. A sufficient condition called almost minimality is given and studied. A weaker necessary condition, being contained a possibly singular real-analytic Levi-flat hypersurface is studied and characterized. This question is completely resolved for algebraic submanifolds of codimension 2 and a sufficient condition for non containment is given for non algebraic submanifolds. As a consequence, an example of a submanifold ofcodimension 2, not biholomorphically equivalent to an algebraic one, is given. We also investigate the structure ofsingularities of Levi-flat hypersurfaces.

Key concepts: Hypersurface, Codimension, Submanifold, Mathematics, Pure mathematics, Holomorphic function, Gravitational singularity, Algebraic number

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