By Bak A. (ed.)

Similar geometry and topology books

The geometry of actual submanifolds in complicated manifolds and the research in their mappings belong to the main complex streams of up to date arithmetic. during this region converge the ideas of assorted and complicated mathematical fields akin to P. D. E. 's, boundary worth difficulties, triggered equations, analytic discs in symplectic areas, advanced dynamics.

New PDF release: Das Zebra-Buch zur Geometrie

In den Niederlanden erscheint seit etwa zehn Jahren die erfolgreiche "Zebra-Reihe" mit Broschüren zu Mathematik fuer Projekte und selbstgesteuertes Lernen. Die Themen sind ohne vertiefte Vorkenntnisse zugänglich und ermöglichen eigenes Erforschen und Entdecken von Mathematik. Die Autoren der Bände sind Schulpraktiker, Mathematikdidaktiker und auch Fachwissenschaftler.

Additional info for Algebraic K-Theory, Number Theory, Geometry and Analysis: Proceedings of July 26-30, 1982

Sample text

Then ~,~ are ambient isometric (by a isometry of CP n) if and only if their directrix curves are equivalent. 26 Proof Suppose the directrix curves are projectively equivalent, ~o - g ~o" say It follows from Theorem 4 and the lemma that g ~0(z) - (adj g)t ~n(-ipf) - (g-1)t ~0(z), so that gig ~0 - ~0" Since ~0 is linearly full g ~ PU(n+I). The converse is trivial. Remark The condition of factoring through RP 2 is crucial here. result is not true in general. [l]). This, together with Theorem 2, is a first step in dealing with the space of minimal immersions of S ~ into Sn.

16) with C a constant. 9) to obtain (n + 2 ) a A a = --(n + 2)c~a" + 3(n -- 1)(a') 2. 1) we get a A a = (A -I~12)a 2. ~(n + 8 ) ~ ) 4--~----~ ] ~ =0. 19) one has 2 ( 4 - n) n2(n +5) 4 T- ~ (a'? - 2-~ = iS ~ - ~ 2 . 20) that a is locally constant on N, which is a contradiction with the definition of U. Hence o~ is constant on M". 1) into 53 consideration, we have (A~)~ = (A -- 1~I2)H, so that either c~ = 0 and M " is minimal or I~12 A and therefore I~12 is constant. But we had at most two different eigenvalues, then because a and lal 2 are constant, such eigenvalues are also constant.

X2k+2 ) = 0. By induction, the first part of the lemma is proved. The proof of the second part is similar, starting from the fact that v2kh = 0 implies that also Y2k+lh = 0. The proof of the following lemma is completely similar to the proof of Lemma 2. Lemma 3 Let M be an equiaffine surface in 0{3 with second fundamental form h. Then v2k+lh = 0 implies that R k + l . vh = 0. The following lemma follows immediately from the skew symmetry of the affine curvature tensor R in its first two components.

### Algebraic K-Theory, Number Theory, Geometry and Analysis: Proceedings of July 26-30, 1982 by Bak A. (ed.)

by Thomas
4.5

Rated 4.25 of 5 – based on 12 votes