By Robert L. Bryant (auth.), Chaohao Gu, Marcel Berger, Robert L. Bryant (eds.)
The DD6 Symposium was once, like its predecessors DD1 to DD5 either a study symposium and a summer time seminar and focused on differential geometry. This quantity features a number of the invited papers and a few extra contributions. They disguise contemporary advances and valuable traits in present examine in differential geometry.
Read or Download Differential Geometry and Differential Equations: Proceedings of a Symposium, held in Shanghai, June 21 – July 6, 1985 PDF
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Additional info for Differential Geometry and Differential Equations: Proceedings of a Symposium, held in Shanghai, June 21 – July 6, 1985
Sample text
Group" by a s y s t e m century, and the s u b s e q u e n t by F. Klein been since groups transformation In the n i n e t e e n t h metry (or m o r e they c l e a r l y of the s y m m e t r i c they simply this groups and d i f f e r e n t i a l has now b e e n e x p a n d e d mathematics. in short, is simply: What geometry was a great into one of the m o s t p r o f o u n d I am t r y i n g let us carry to say on this in fascinating tradition! Generally models". which speaking, In a way, studies examples, structures with profound scientific to c o m m a n d natural of are faced w i t h of t h e m mixture kinds analogous vast For varieties It seems need quite some and complexities beauties, *) R e s e a r c h p a r t i a l l y s u p p o r t e d by NSF Grant and A l e x a n d e r - v o n - H u m b o l d t - S t i f t u n g of endowed to d e v e l o p to c o m p r e h e n d of v a r i e t i e s , "space- to biology, "organisms".
M i n i m a l immersions of compact irreducible homogeneous R i e m a n n i a n m a n i f o l d s into spheres Let M be a compact i r r e d u c i b l e R i e m a n n i a n manifold. Fix xoEM. Let H be the isotropic s u b g r o u p of isometrics on M with respect to x o, H ° the identity c o m p o n e n t of H, and PHo={x~Mlhx=x, A s s u m e now ~:M+sn(r) the image for any h~H°}. to be a minimal isometric immersion, By [5], ~(M)=N with the induced R i e m a n n i a n structure is also an ir- reducible h o m o g e n e o u s R i e m a n n i a n manifold.
Can be d e c o m p o s e d For each the v a r i a t i o n a l point X 1 6 V, cocompleteness , to be the c o d i m e n s i o n fields in the space Bott and S a m e l s o n a more systematic of the focal will Lie variety certainly structure structure of the pair will no exotic spheres 2: G e o m e t r y Roughly speaking, associated of points. geometries, and, of c o n g r u e n c e a triangle three damental compact Or does special cases, on t o p o l o g i c a l it is a c t u a l l y of those exotic equal interval object spheres to I.