Conformal deformations of prescribing scalar curvature on Riemannian manifolds with negative curvature

1998 ◽  
Vol 14 (3) ◽  
pp. 361-370
Author(s):  
Hu Zejun
Keyword(s):  
Scalar Curvature ◽  
Riemannian Manifolds ◽  
Negative Curvature ◽  
Conformal Deformations

On the conformal scalar curvature equations on Finsler manifolds

2016 ◽  
Vol 14 (01) ◽  
pp. 1750008
Author(s):  
Neda Shojaee ◽  
Morteza MirMohammad Rezaii
Keyword(s):  
Scalar Curvature ◽  
Finsler Geometry ◽  
Yamabe Problem ◽  
Finsler Manifolds ◽  
Yamabe Flow ◽  
Conformal Deformations

In this paper, we study conformal deformations and [Formula: see text]-conformal deformations of Ricci-directional and second type scalar curvatures on Finsler manifolds. Then we introduce the best equation to study the Yamabe problem on Finsler manifolds. Finally, we restrict conformal deformations of metrics to [Formula: see text]-conformal deformations and derive the Yamabe functional and the Yamabe flow in Finsler geometry.

Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows

1989 ◽  
Vol 9 (3) ◽  
pp. 427-432 ◽  
Author(s):  
Renato Feres ◽  
Anatoly Katok
Keyword(s):  
Dynamical Systems ◽  
Lyapunov Exponents ◽  
Riemannian Manifolds ◽  
Negative Curvature ◽  
Geodesic Flows ◽  
Tensor Fields ◽  
Invariant Tensor ◽  
Affine Connections

AbstractWe consider in this note smooth dynamical systems equipped with smooth invariant affine connections and show that, under a pinching condition on the Lyapunov exponents, certain invariant tensor fields are parallel. We then apply this result to a problem of rigidity of geodesic flows for Riemannian manifolds with negative curvature.

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