Author Hennes, Peter
Title Weierstrass representations of minimal real Kahler submanifolds
book jacket
Descript 77 p
Note Source: Dissertation Abstracts International, Volume: 63-04, Section: B, page: 1876
Adviser: Detlef Gromoll
Thesis (Ph.D.)--State University of New York at Stony Brook, 2001
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
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
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
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
School code: 0771
Host Item Dissertation Abstracts International 63-04B
Subject Mathematics
Alt Author State University of New York at Stony Brook