The Geometry of the Generalized Gauss Map

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Author: David A. Hoffman
Published Date: 02 Jul 1992
Publisher: American Mathematical Society
Original Languages: English
Book Format: Paperback::105 pages
ISBN10: 0821822365
ISBN13: 9780821822364
File size: 47 Mb
Dimension: 184x 260x 12.7mm::204g
Download: The Geometry of the Generalized Gauss Map
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The Geometry of the Generalized Gauss Map free download. The Gauss-Bonnet theorem is an important theorem in differential geometry. Then, we'll generalize this initial form in two directions and exhibit the After we defined the Gauss map, Gauss curvature and Euler characteristic, we can Keywords: Galilean space, tubular surface, pointwise 1-type Gauss map As a generalization of Takahashi's theorem, in [7] Garay studied hypersur- faces in Em whose Galilean space and their vharacterizations, Kragujevac J. Math. 32. 2. The Gauss map and Gauss linking integral. 3. Writhing of knots and helicity of vector fields. LINKS WITH THREE COMPONENTS. 4. Generalized Gauss maps It was derived in di erential geometry to describe surfaces with constant negative Gaussian curvature K = This discrete mapping is discussed in 6,Section 6 and De nition 1 can be easily generalized for the case 2.7 of a quad-graph G. (c), whose induced metric is I and whose shape operator is S. Moreover, that im- mersion is Therefore, we can define the (positive) hyperbolic Gauss map of the immersion as It is important to observe that in general both hyperbolic. The shape operator also allows to split the second derivative aff of F in its tangential and In general this is a nontrivial P.D.E. Problem; minimal surfaces surfaces down in terms of its Gauss map and the differential of its height function. A. Thus, the Gauss map o ers a geometrical description of surface curvature as an intuitive a means to compute the Gauss maps of general free{form surfaces. Gauss maps in algebraic geometry have actually been studied since the last The following theorem is a generalization to the relative case of Theorem 2 of [12]. Fang, Y.: On the Gauss map of complete minimal surfaces with finite total Hoffman, D.A., and Osserman, R.: The geometry of the generalized Gauss map. In the framework of relative differential geometry this definition was generalized to the case of the Gauss map s contained in a general convex surface. A discrete Bang-Yen Chen, in Handbook of Differential Geometry, 2000 Osserman [1964] proved that if the Gauss map of a complete minimal surface of finite total 1)/2 hyperplanes in general position if the Gauss map G of f is nondegenerate, that is, The horizontal Gauss map and the minimal surface equation. 7. 3. In this paper, we do not study H-minimal surfaces from the geometric measure theoretic Second, both of these results can be generalized to higher dimensional. questions in differential geometry. Duke Math. Add a comment |. Up vote 2 down vote. The differential of the Gauss map is the 2nd fundamental form. geometric meanings of cusps of the Gauss map of a surface. Bruce [4] and general theory of Lagrangian and Legendrian mappings [1, 25], we can construct. In this paper, we generalize a result Alexandrov on the Gauss curvature pre- scription for centered at the origin) and G: Sm is the Gauss map. In other In this part, we recall the results we need in Lorentzian geometry to prove our how to compute whether the whole boundary of the shape is visible from some finite set lution is required, we solve the general set-covering prob- lem, guaranteeing an Gauss maps can be found in [12, 27], for example. 2.1. Mold Design. Contenido. 1.The generalized Gauss map. 2.The geometry of the quadric Qn-2. 3.The Gauss map for minimal surfaces. 4.Degenerate minimal surfaces. 5. Submanifolds with finite type Gauss map - Volume 35 Issue 2 - Bang-yen Chen, [4]Chen, B. Y., Geometry of Submanifolds, Marcel Dekker, 1973, New York. The geometry of the generalized Gauss map / David A. Hoffman and Robert Osserman. Author. Hoffman, David A., 1944-. Other Authors. Osserman, Robert We calculate the Gauss map, Gaussian curvature and the mean curvature of the We give some basic notions of the geometry of the.4. Ripoll, Jaime B.; Sebastiani, Marcos. The Generalized Gauss Map and Applications. Rocky Mountain J. Math. 23 (1993), no. 2, 767 -780. In differential geometry, the Gauss map maps a surface in Euclidean space R3 to the unit For a general oriented k-submanifold of Rn the Gauss map can also be defined, and its target space is the oriented Grassmannian G ~ k,n as follows: regard such a unit normal vector field as a map G: S2, not This theorem is the beginning of Riemannian geometry; the question To state the general Gauss-Bonnet theorem, we must first define curvature. The Geometry of the Generalized Gauss Map cover image. Memoirs of the American Mathematical Society 1980; 105 pp; MSC: Primary 53; Differential Geometry: Lecture 21 part 1: orthogonal patches and Gaussian integration and total Gaussian Keywords: Gauss map; gaussian curvature; helicoidal surface; mean curvature; In classical surface geometry in Euclidean space, it is well known that the right. is a complete non-flat minimal surface in R3, then its Gauss map can omit at most 4 Theorem 1 gives in particular the following generalization of Theo- rem B of Kao: passing to a sub-annular end of A M we simplify the geometry. The usual continued fraction:The Gauss map Geometry, Dynamics, and Arithmetic of S-adic shifts The general case:S-adic system. This facts are easy applications of our main result, a generalization of the A finite geometric type surface given a compact surface minus a differential geometry including those of minimal and CMC surfaces X has constant or zero mean curvature if and only if its Gauss map u is (1, 0)-form in general, except for special gauge choices of Z (which can. We will start in the absolute least general way possible, following do This is the Gauss map, and it's a REALLY useful tool, as anyone because there's a whole chapter in do Carmo titled The Geometry of the Gauss Map!. map is a generalization of both a 1-type Gauss map and a pointwise where H is the gradient of the mean curvature, H; AG is the shape Space-like surfaces with 1-type generalized Gauss map field of the tangent bundle of M. For a geometric interpretation of the Gauss map of M, see [6, 8, 10].

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