By Thomas E. Cecil, Shiing-Shen Chern (auth.), Boju Jiang, Chia-Kuei Peng, Zixin Hou (eds.)

From the contents: T.E. Cecil, S.S. Chern: Dupin Submanifolds in Lie Sphere Geometry.- R.L. Cohen, U. Tillmann: Lectures on Immersion Theory.- Li An-Min: Affine Maximal floor and Harmonic Functions.- S. Murakami: unheard of easy Lie teams and comparable themes in contemporary Differential Geometry.- U. Simon: Dirichlet difficulties and the Laplacian in Affine Hypersurface Theory.- Wang Shicheng: crucial Invariant Circles of floor Automorphism of Finite Order.

Show description

Read or Download Differential Geometry and Topology: Proceedings of the Special Year at Nankai Institute of Mathematics, Tianjin, PR China, 1986–87 PDF

Similar geometry books

Conceptual Spaces: The Geometry of Thought

Inside cognitive technological know-how, methods presently dominate the matter of modeling representations. The symbolic method perspectives cognition as computation concerning symbolic manipulation. Connectionism, a unique case of associationism, versions institutions utilizing synthetic neuron networks. Peter Gardenfors bargains his thought of conceptual representations as a bridge among the symbolic and connectionist methods.

The Art of the Intelligible (survey of mathematics in its conceptual development)

A compact survey, on the trouble-free point, of a few of the main very important thoughts of arithmetic. consciousness is paid to their technical good points, old improvement and broader philosophical value. all the a variety of branches of arithmetic is mentioned individually, yet their interdependence is emphasized all through.

Der Goldene Schnitt

Der Goldene Schnitt tritt seit der Antike in vielen Bereichen der Geometrie, Architektur, Musik, Kunst sowie der Philosophie auf, aber er erscheint auch in neueren Gebieten der Technik und der Fraktale. Dabei ist der Goldene Schnitt kein isoliertes Phänomen, sondern in vielen Fällen das erste und somit einfachste nichttriviale Beispiel im Rahmen weiterführender Verallgemeinerungen.

Complex Manifolds and Hyperbolic Geometry: II Iberoamerican Congress on Geometry, January 4-9, 2001, Cimat, Guanajuato, Mexico

This quantity derives from the second one Iberoamerican Congress on Geometry, held in 2001 in Mexico on the Centro de Investigacion en Matematicas A. C. , an across the world well-known software of analysis in natural arithmetic. The convention subject matters have been selected with an eye fixed towards the presentation of latest equipment, fresh effects, and the construction of extra interconnections among the several learn teams operating in complicated manifolds and hyperbolic geometry.

Extra resources for Differential Geometry and Topology: Proceedings of the Special Year at Nankai Institute of Mathematics, Tianjin, PR China, 1986–87

Example text

Now we want to attach a locally smooth frame field to the unit normal bundle ~'(N). In fact, we only need to assign a frame {x; a A} for each unit normal vector v = ha ea(x) where x e u and ~(%a)2 = i such that 52 a z. = e . e. a = 0. Evidently m rn we can choose u ~ smoothly on x i and %a . 13) . 14) to {a A} along connection Before doing Yv(S)=exp~(s'V) in M, then we obtain a locally {EA(E)} on the tubular hypersurface dual coframe. the geodisic smooth Ng. The aim of §2 is to find its so we should recall some facts about the N-Jacobi field.

23) for some integer m. 12). 2a) 4 A ~2 + (-p 5 = - ~1 5 i) A (-q ~1-t 4 3 1-u ~7) 3 4 ~ 5 ho ~)7 A ( b ~ 1 + c ~ ) + ( a ~ 4 + b ~ 1 ) A I ~1 . 29) = 1 i + db A . 29) ~4 + a(,,) 1 A + b(~ i 5 - p 3 1 A ,,,,) ) ^ ~51- p . ~ ^ . 19) and A ~5 = 0 . 24) d e + 2b ~}I1 = clP3 + 2/o3 ¢a11 = P 3 1 e l that + P3262 + P33e3 . 33) 5 (da + 2a e~- e27 - 2-4)b3 4 (pt + P31)el ) A e l 3 only. + terms involving t#5 1 and ~7 Thus - the ' 4 a~ 1. 21) of 4 1' call it as da + 2 a ta~ = e27 + aO 1 + (P31-PP2)8 2 + 2PP3O 3 .

Frame which we w i l l need ill t h i s case p # 0. So, we again drop the a s t e r i s k s . We are now ready to prove P i n k a l l ' s c l a s s i f i c a t i o n r e s u l t f o r the case p ~ 0 [P2, p. 117]. As with the c y c l i d e s , t h e r e i s only one compact model, up to Lie equivalence. This i s C a r t a n ' s isoparametric hypersurface M 3 in S4. ) surfaces in S4. (See two focal submanifolds, which [CR, pp. 296-299] for (Pinkall is contained [P2]): (a) E v e r y c o n n e c t e d Dupln s u b m a n i f o l d w i t h p # 0 i n a u n i q u e c o m p a c t c o n n e c t e d Dupin s u b m a n i f o l d w i t h p # 0.

Download PDF sample

Rated 4.24 of 5 – based on 4 votes