Displaying similar documents to “Geodesics on a central symmetric warped product manifold.”

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...

Characterizations of complex space forms by means of geodesic spheres and tubes

J. Gillard (1996)

Colloquium Mathematicae

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We prove that a connected complex space form ( M n ,g,J) with n ≥ 4 can be characterized by the Ricci-semi-symmetry condition R ˜ X Y · ϱ ˜ = 0 and by the semi-parallel condition R ˜ X Y · σ = 0 , considering special choices of tangent vectors X , Y to small geodesic spheres or geodesic tubes (that is, tubes about geodesics), where R ˜ , ϱ ˜ and σ denote the Riemann curvature tensor, the corresponding Ricci tensor of type (0,2) and the second fundamental form of the spheres or tubes and where R ˜ X Y acts as a derivation.

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...