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001    AAI3051066 
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008    100520s2001    ||||||||||||||||| ||eng d 
020    9780493653921 
035    (UMI)AAI3051066 
040    UMI|cUMI 
100 1  Hennes, Peter 
245 10 Weierstrass representations of minimal real Kahler 
       submanifolds 
300    77 p 
500    Source: Dissertation Abstracts International, Volume: 63-
       04, Section: B, page: 1876 
500    Adviser:  Detlef Gromoll 
502    Thesis (Ph.D.)--State University of New York at Stony 
       Brook, 2001 
520    Since the nineteenth century, Weierstrass representations 
       have been used to investigate minimal surfaces in 
       Euclidean 3-space. In the last two decades, it emerged 
       that minimal Kahler submanifolds of Euclidean spaces share
       many of the features of minimal surfaces. In this 
       dissertation, we try to find similar representations for 
       these minimal real Kahler submanifolds 
520    First, we modify a method developed by M. Dajczer and D. 
       Gromoll to give a simple way of describing minimal real 
       Kahler hypersurfaces. As an application, we are able to 
       give local examples of superminimal surfaces in the 4-
       sphere 
520    Then, based on the formulae for the classical Weierstrass 
       representation, we find a coordinate system for the 
       homogeneous space of all isotropic complex planes in 
       arbitrary complex vector spaces of dimension at least 5. 
       We utilize this coordinate system to give a local 
       characterization of minimal real Kahler surfaces (of real 
       dimension 4) in Euclidean spaces 
520    Finally, using this characterization, we are able to give 
       a complete local classification and construction methods 
       for all minimal real Kahler surfaces in Euclidean 6-space,
       at least away from certain isolated singularities. 
       Employing these construction methods, we also give some 
       explicit new examples for such submanifolds 
590    School code: 0771 
650  4 Mathematics 
690    0405 
710 2  State University of New York at Stony Brook 
773 0  |tDissertation Abstracts International|g63-04B 
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