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Classification of Twistor Spaces with a Pencil of Surfaces of Degree 1, Part I
Author(s) -
Kurke Herbert
Publication year - 1992
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19921580105
Subject(s) - twistor theory , pencil (optics) , twistor space , mathematics , pure mathematics , class (philosophy) , projective plane , degree (music) , transversal (combinatorics) , algebra over a field , mathematical analysis , geometry , physics , computer science , artificial intelligence , acoustics , correlation , quantum mechanics
We display a family of compact complex 3‐manifolds which yields all twistor spaces containing a pencil of surfaces transversal to the twistor lines. This also yields explicit families of self‐dual metrics on connected sums of complex projective planes. This yields a completely alternative approach to a class of such metrics which was recently found by Claude le Brun [11].