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The Geometry of the Generalized Gauss Map
David A. HoffmanRobert Osserman
出版American Mathematical Soc., 1980
主題Mathematics / Geometry / Differential
ISBN08218223659780821822364
URLhttp://books.google.com.hk/books?id=Dx3UCQAAQBAJ&hl=&source=gbs_api
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註釋This paper is devoted primarily to the study of properties of the Grassmannian of oriented 2-planes in [double-struck capital]R[superscript]n and to applications of these properties to understanding minimal surfaces in [double-struck capital]R[superscript]n via the generalized Gauss map. The extrinsic geometry of the Grassmannian, when considered as a submanifold of [double-struck capital]CP[superscript]n-2, is investigated, with special emphasis on the nature of the intersection of the Grassmannian with linear subspaces of [double-struck capital]CP[superscript]n-1. These results are the basis for a discussion of minimal surfaces that are degenerate in various ways; understanding the different types of degeneracy and their interrelations is a critical step toward obtaining a clear picture of the basic geometric properties of minimal surfaces in [double-struck capital]R[superscript]n.