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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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