By K. Leichtweiß (auth.), Dirk Ferus, Wolfgang Kühnel, Udo Simon, Bernd Wegner (eds.)

ISBN-10: 354010285X

ISBN-13: 9783540102854

ISBN-10: 3540384197

ISBN-13: 9783540384199

**Read Online or Download Global Differential Geometry and Global Analysis: Proceedings of the Colloquium Held at the Technical University of Berlin, November 21 – 24, 1979 PDF**

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**Extra info for Global Differential Geometry and Global Analysis: Proceedings of the Colloquium Held at the Technical University of Berlin, November 21 – 24, 1979**

**Example text**

The n o t i o n line element~ circa superficies first to later, der of w a s made curves". isolate after intrinsic clear (See page and understand B. I". } of notion revolutionary iiegen", one of In say deduced "Ubcr that from he was the A quarter die of a century ~typothesen, Riemannian a generales particular curvature. address can as "l)iseuisitiones welche geometry was founded. On t h e ingredients fel wax t h e the metric ordinary other first were to the absolute diff~rentiel his student completed m ake a v a i l a b l e ly clear in ]900 to exposition modern this played by text the cover]ant derivation the of theory, one of a connection.

Let A(G),A(H),A(K) be the corresponding Lie algebras, and choose some ad(H)-invariant complement P of A(H) in A(G), some ad(K)-invariant complement Q of A(K) in A(H). Then any ad(H)-invariant scalar product on P gives rise to a G-invariant metric h on G/H; similarly any ad(K)-invariant scalar product on Q gives rise to a H-invariant metric on H/K. Now if g is the G-invariant metric on G/K corresponding to the scalar product on P @ Q given by the two preceding scalar products on P and Q and the condition that P and Q are orthogonal, then~rg is a Riemannian submersion from (G/K,g) onto (G/H,h) with totally geodesic fibres isometric to (H/K,k).

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### Global Differential Geometry and Global Analysis: Proceedings of the Colloquium Held at the Technical University of Berlin, November 21 – 24, 1979 by K. Leichtweiß (auth.), Dirk Ferus, Wolfgang Kühnel, Udo Simon, Bernd Wegner (eds.)

by David

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