The Geometry Of The Generalized Gauss Map
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The Geometry Of The Generalized Gauss Map
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Author : David A. Hoffman
language : en
Publisher: American Mathematical Soc.
Release Date : 1980
The Geometry Of The Generalized Gauss Map written by David A. Hoffman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Mathematics categories.
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.
Grassmannians And Gauss Maps In Piecewise Linear Topology
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Author : Norman Levitt
language : en
Publisher: Springer
Release Date : 2006-11-14
Grassmannians And Gauss Maps In Piecewise Linear Topology written by Norman Levitt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
The book explores the possibility of extending the notions of "Grassmannian" and "Gauss map" to the PL category. They are distinguished from "classifying space" and "classifying map" which are essentially homotopy-theoretic notions. The analogs of Grassmannian and Gauss map defined incorporate geometric and combinatorial information. Principal applications involve characteristic class theory, smoothing theory, and the existence of immersion satifying certain geometric criteria, e.g. curvature conditions. The book assumes knowledge of basic differential topology and bundle theory, including Hirsch-Gromov-Phillips theory, as well as the analogous theories for the PL category. The work should be of interest to mathematicians concerned with geometric topology, PL and PD aspects of differential geometry and the geometry of polyhedra.
Differential Geometry Of Varieties With Degenerate Gauss Maps
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Author : Maks A. Akivis
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-18
Differential Geometry Of Varieties With Degenerate Gauss Maps written by Maks A. Akivis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-18 with Mathematics categories.
This book surveys the differential geometry of varieties with degenerate Gauss maps, using moving frames and exterior differential forms as well as tensor methods. The authors illustrate the structure of varieties with degenerate Gauss maps, determine the singular points and singular varieties, find focal images and construct a classification of the varieties with degenerate Gauss maps.
Generalized Curvatures
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Author : Jean-Marie Morvan
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-13
Generalized Curvatures written by Jean-Marie Morvan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-13 with Mathematics categories.
The central object of this book is the measure of geometric quantities describing N a subset of the Euclidean space (E ,), endowed with its standard scalar product. Let us state precisely what we mean by a geometric quantity. Consider a subset N S of points of the N-dimensional Euclidean space E , endowed with its standard N scalar product. LetG be the group of rigid motions of E . We say that a 0 quantity Q(S) associated toS is geometric with respect toG if the corresponding 0 quantity Q[g(S)] associated to g(S) equals Q(S), for all g?G . For instance, the 0 diameter ofS and the area of the convex hull ofS are quantities geometric with respect toG . But the distance from the origin O to the closest point ofS is not, 0 since it is not invariant under translations ofS. It is important to point out that the property of being geometric depends on the chosen group. For instance, ifG is the 1 N group of projective transformations of E , then the property ofS being a circle is geometric forG but not forG , while the property of being a conic or a straight 0 1 line is geometric for bothG andG . This point of view may be generalized to any 0 1 subsetS of any vector space E endowed with a groupG acting on it.
Value Distribution Theory Of The Gauss Map Of Minimal Surfaces In Rm
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Author : Hirotaka Fujimoto
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Value Distribution Theory Of The Gauss Map Of Minimal Surfaces In Rm written by Hirotaka Fujimoto and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book presents in a systematic and almost self-contained way the striking analogy between classical function theory, in particular the value distribution theory of holomorphic curves in projective space, on the one hand, and important and beautiful properties of the Gauss map of minimal surfaces on the other hand. Both theories are developed in the text, including many results of recent research. The relations and analogies between them become completely clear. The book is written for interested graduate students and mathematicians, who want to become more familiar with this modern development in the two classical areas of mathematics, but also for those, who intend to do further research on minimal surfaces.
Differential Geometry
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Author : Wolfgang Kühnel
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-12-22
Differential Geometry written by Wolfgang Kühnel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-22 with Mathematics categories.
This carefully written book is an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. The second part studies the geometry of general manifolds, with particular emphasis on connections and curvature. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra. This new edition provides many advancements, including more figures and exercises, and--as a new feature--a good number of solutions to selected exercises.
Harmonic Maps
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Author : James Eells
language : en
Publisher: World Scientific
Release Date : 1992
Harmonic Maps written by James Eells and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
These original research papers, written during a period of over a quarter of a century, have two main objectives. The first is to lay the foundations of the theory of harmonic maps between Riemannian Manifolds, and the second to establish various existence and regularity theorems as well as the explicit constructions of such maps.
The Geometry Of Submanifolds
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Author : Yu. Aminov
language : en
Publisher: CRC Press
Release Date : 2001-01-11
The Geometry Of Submanifolds written by Yu. Aminov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-11 with Mathematics categories.
This is a comprehensive presentation of the geometry of submanifolds that expands on classical results in the theory of curves and surfaces. The geometry of submanifolds starts from the idea of the extrinsic geometry of a surface, and the theory studies the position and properties of a submanifold in ambient space in both local and global aspects.
Pointwise 1 Type Gauss Map Os Developable Smarandache Rules Surfaces
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Author : Stuti Tamta
language : en
Publisher: Infinite Study
Release Date : 2023-01-01
Pointwise 1 Type Gauss Map Os Developable Smarandache Rules Surfaces written by Stuti Tamta and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Mathematics categories.
In this paper, we study the developable TN, TB, and NB-Smarandache ruled surface with a pointwise 1-type Gauss map. In particular, we obtain that every developable TN-Smarandache ruled surface has constant mean curvature, and every developable TB-Smarandache ruled surface is minimal if and only if the curve is a place curve with non-zero curvature or a helix, and every developable NB-Smarandache ruled surface is always plane. We also provide some examples.
Geometry Symposium Utrecht 1980
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Author : E. Looijenga
language : en
Publisher: Springer
Release Date : 2006-11-14
Geometry Symposium Utrecht 1980 written by E. Looijenga and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.