Unique determination of multidimensional submanifolds of Euclidean space from the Grassman image

1992 ◽  
Vol 51 (1) ◽  
pp. 6-11 ◽  
Author(s):  
A. A. Borisenko
Keyword(s):  
Euclidean Space ◽  
Unique Determination

scholarly journals A note on surfaces with prescribed oriented Euclidean Gauss map

2005 ◽  
Vol 2005 (4) ◽  
pp. 537-543
Author(s):  
Ricardo Sa Earp ◽  
Eric Toubiana
Keyword(s):  
Euclidean Space ◽  
Hyperbolic Space ◽  
Gauss Map ◽  
Compatibility Relation ◽  
Hyperbolic Gauss Map ◽  
Conformal Immersion

We present another proof of a theorem due to Hoffman and Osserman in Euclidean space concerning the determination of a conformal immersion by its Gauss map. Our approach depends on geometric quantities, that is, the hyperbolic Gauss mapGand formulae obtained in hyperbolic space. We use the idea that the Euclidean Gauss map and the hyperbolic Gauss map with some compatibility relation determine a conformal immersion, proved in a previous paper.

Two problems in the theory of unique determination of domains

2012 ◽  
Vol 188 (4) ◽  
pp. 463-473
Author(s):  
D. A. Slutskii
Keyword(s):  
Unique Determination

On unique determination of domains in Euclidean spaces

2008 ◽  
Vol 153 (6) ◽  
pp. 869-898 ◽  
Author(s):  
A. P. Kopylov
Keyword(s):  
Unique Determination ◽  
Euclidean Spaces
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