Descript 
77 p 
Note 
Source: Dissertation Abstracts International, Volume: 6304, 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 3space. 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 4sphere 

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 6space, 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 6304B

Subject 
Mathematics


0405

Alt Author 
State University of New York at Stony Brook

