Displaying similar documents to “Splitting theorems of riemannian manifolds”

Geodesic graphs on special 7-dimensional g.o. manifolds

Zdeněk Dušek, Oldřich Kowalski (2006)

Archivum Mathematicum

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In ( Dušek, Z., Kowalski, O. and Nikčević, S. Ž., New examples of Riemannian g.o. manifolds in dimension 7, Differential Geom. Appl. 21 (2004), 65–78.), the present authors and S. Nikčević constructed the 2-parameter family of invariant Riemannian metrics on the homogeneous manifolds M = [ SO ( 5 ) × SO ( 2 ) ] / U ( 2 ) and M = [ SO ( 4 , 1 ) × SO ( 2 ) ] / U ( 2 ) . They proved that, for the open dense subset of this family, the corresponding Riemannian manifolds are g.o. manifolds which are not naturally reductive. Now we are going to investigate the remaining...

Lorentzian geometry in the large

John Beem (1997)

Banach Center Publications

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Lorentzian geometry in the large has certain similarities and certain fundamental differences from Riemannian geometry in the large. The Morse index theory for timelike geodesics is quite similar to the corresponding theory for Riemannian manifolds. However, results on completeness for Lorentzian manifolds are quite different from the corresponding results for positive definite manifolds. A generalization of global hyperbolicity known as pseudoconvexity is described. It has important...