Download Geometry Symposium Utrecht 1980: Proceedings of a Symposium by P. Baird, J. Eells (auth.), E. Looijenga, D. Siersma, F. PDF

By P. Baird, J. Eells (auth.), E. Looijenga, D. Siersma, F. Takens (eds.)

Show description

Read Online or Download Geometry Symposium Utrecht 1980: Proceedings of a Symposium Held at the University of Utrecht, The Netherlands, August 27–29, 1980 PDF

Similar geometry books

Laplacian on Riemannian manifold

This article on research on Riemannian manifolds is an intensive creation to subject matters lined in complex learn monographs on Atiyah-Singer index idea. the most topic is the examine of warmth circulation linked to the Laplacians on differential types. this gives a unified remedy of Hodge idea and the supersymmetric facts of the Chern-Gauss-Bonnet theorem.

Geometry of Sporadic Groups II: Representations and Amalgams (Encyclopedia of Mathematics and its Applications 91)

This moment quantity in a two-volume set offers an entire self-contained facts of the type of geometries linked to sporadic uncomplicated teams: Petersen and tilde geometries. It features a learn of the representations of the geometries into consideration in GF(2)-vector areas in addition to in a few non-Abelian teams.

Geometric Computations with Interval and New Robust Methods: Applications in Computer Graphics, GIS and Computational Geometry

This undergraduate and postgraduate textual content will familiarise readers with period mathematics and comparable instruments to achieve trustworthy and proven effects and logically right judgements for numerous geometric computations, and the ability for relieving the consequences of the mistakes. It additionally considers computations on geometric point-sets, that are neither powerful nor trustworthy in processing with typical tools.

Extra resources for Geometry Symposium Utrecht 1980: Proceedings of a Symposium Held at the University of Utrecht, The Netherlands, August 27–29, 1980

Example text

Let X : M2 > ~4 be a smooth immersion of a surface without boundary, not necessarily orientable, into vectors given by ~*X : M2 V in ~(Z) for 4-space. e. the composition will have a finite number of singularities where the rank of not 2 . These singularities occur at points lies in the tangent plane to X(M 2) at X(u) . In order for X , we require further that for each singular point of a small disc about u in M2 u u of M2 such that V to be general the image under ~oX will be topologically a cone over a figure eight, a singularity known as a Whitney pinch point or an umbrella point.

The results of Section conditions | and 2 in order to formu- for the existence of a minimal hypersurfa- 52 I. The Ricci C o n d i t i o n and its Generalizations. We start by d i s c u s s i n g the classical result of Ricci for minimal surfaces in E 3 . I. Let any point of M M where the Gauss curvature i) the metric is negative, has constant curvature ds g = #-K ds 2 iii) the curvature K ds 2 . T h e n at the following three con- K m | ; has constant curvature Km 0 ; satisfies (I) A log(-K) = 4K , where Proof K En : d~ 2 = - Kds 2 ii) the metric .

I 13 J (uij) = ,e) (u B) , ,e i) spaces : e' = l ~ u~seB are orthogonal matrices, m~l~ = (del'e~) = Z uiju 8wjB ~! oJ. m. i i~ = Z are called the second fundamental forms. ~. lJ~ i J h.. If then ll(v) = Z v II is the second fundamental form in the direction v ; the second fundamental form is 65 thus a normal-valued quadratic differential form. , (23a) Z h.. = 0 = if 0 . equations dm. = Z ~. A ~.. z j JZ which shows that Civita (mij) connection, (5) in three sets v . if of the other structure (24) in the normal vector IIfX i The pull-back , defines , the torsionless in the tangent in (4) gives bundle.

Download PDF sample

Rated 4.39 of 5 – based on 32 votes