scholarly journals Some corrections to: ``Closed geodesics on certain Riemannian manifolds of positive curvature''

1969 ◽  
Vol 21 (4) ◽  
pp. 674-675
Author(s):  
Yôtarô Tsukamoto
Keyword(s):  
Riemannian Manifolds ◽  
Positive Curvature ◽  
Closed Geodesics

Closed geodesics in Riemannian manifolds with convex boundary

1994 ◽  
Vol 124 (6) ◽  
pp. 1247-1258 ◽  
Author(s):  
Anna Maria Candela ◽  
Addolorata Salvatore
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Closed Geodesics ◽  
Convex Boundary

In this paper we look for closed geodesies on a noncomplete Riemannian manifold ℳ. We prove that if ℳ has convex boundary, then there exists at least one closed nonconstant geodesic on it.

scholarly journals Cohomogeneity one Riemannian manifolds of non-positive curvature

2007 ◽  
Vol 25 (5) ◽  
pp. 561-581 ◽  
Author(s):  
H. Abedi ◽  
D.V. Alekseevsky ◽  
S.M.B. Kashani
Keyword(s):  
Riemannian Manifolds ◽  
Positive Curvature ◽  
Cohomogeneity One

scholarly journals A Kähler Einstein structure on the tangent bundle of a space form

2001 ◽  
Vol 25 (3) ◽  
pp. 183-195 ◽  
Author(s):  
Vasile Oproiu
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Tangent Bundle ◽  
Negative Curvature ◽  
Space Form ◽  
Positive Curvature ◽  
Holomorphic Sectional Curvature ◽  
Zero Section ◽  
Constant Negative Curvature ◽  
Constant Positive Curvature

We obtain a Kähler Einstein structure on the tangent bundle of a Riemannian manifold of constant negative curvature. Moreover, the holomorphic sectional curvature of this Kähler Einstein structure is constant. Similar results are obtained for a tube around zero section in the tangent bundle, in the case of the Riemannian manifolds of constant positive curvature.

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