By Atsushi Kasue (auth.), K. Kenmotsu (eds.)
Read Online or Download Differential Geometry of Submanifolds: Proceedings of the Conference held at Kyoto, January 23–25, 1984 PDF
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A tour of subriemannian geometries, their geodesics and applications
Subriemannian geometries, sometimes called Carnot-Caratheodory geometries, will be considered as limits of Riemannian geometries. in addition they come up in actual phenomenon concerning ""geometric phases"" or holonomy. Very approximately conversing, a subriemannian geometry includes a manifold endowed with a distribution (meaning a $k$-plane box, or subbundle of the tangent bundle), referred to as horizontal including an internal product on that distribution.
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Additional info for Differential Geometry of Submanifolds: Proceedings of the Conference held at Kyoto, January 23–25, 1984
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Of T is equivalent and (3) m(1)+l ¢2 ) to In case of @ • v (p,q) = (6,3) and ~l+l (4,4) 35 ~2+i 84 70 in this case ¢i stan- (P~q~3). v ¢i (resp. sine Y) 105). (o~e~w/2) minimal into ~I to and sine 0 = and Z2 immersion result the first from 7, Proposition 5, ¢I 6(2), is linearly Case (resp. Lemma rigid. By (3) of Lemma 13. standard of S0(9)/S(0(6)x0(3)) In other words a of sm(1)(1). and Theorem (resp. d. (1) (2) ¢2 = 128 inequivalent Proof of Theorem A. ii, Lemma 10(3), Lemma imal immersion second) cos@ 0 = (ZI+I/~I+~2+2) I/2 (SO(p+q)/SO(p)xSO(q),(Xl/pq)g0) S0(6)xS0(3) (resp.
I. The standard minimal In this immersions section we explane the c o s t r u c t i o n of the standard minimal immersions and their properties Let M = G/K be an n - d i m e n s i o n a l compact type. (G,K) ple Lie group. We denote by K, respectively. induced by (cf. Wallach Let go ~ and operator of (M,g 0) M. , the set of all m u t u a l l y distinct For each integer basis of k Vk £ symmetric space of is a compact the Lie algebra of B of g. Let A a c t i n g on the space We denote by eigenvalues with the eigenvalue k~l, let G G semisimand be the G-invariant R i e m a n n i a n metric on all r e a l - v a l u e d C ~ - f u n c t i o n s on the eigenspace of irreducible is a symmetric pair and (-l)-times the Killing form Laplace-Beltrami [16]).
Parry and M. ~llicott; An analogue of the prime number theo- rem for closed orbits of Axiom A flows, Ann. of Math. I18(1983), 573-591. L. ables, [25] Royden; The A h l f o r s - S c h w a r z Comment. Math. Helv. R. T. Yau; of manifolds lemma in several 55(1980), Compact with non-positive complex vari- 547-558. group actions curvature, and the topology Topology 18(1979), 361- 380. [26] T. Sunada; Holomorphic mappings symmetric bounded domain, [27] T. Sunada; 51(1979), Rigidity 297-307. into a compact quotient Nagoya Math.