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complete riemannian manifold
 
cut locus
 
exponential map
 

 

 

 

 

 

 

 
 
 
 
 
 
 
When M is simply connected, the convexity radius of M is ? iff M There exist examples of manifolds with focal points but without conjugate points. by your definition (simply connected and without conjugate points), but,
 13 Jun 2012 We define the injectivity radius growth by ?(M) = lim r>? The last section contains some examples and questions. Acknowledgements The
 14 Apr 2016 arxiv.org/abs/math/0001108# This paper by Schick is nicely written and contains coordinate-wise and coordinate-free definitions of
 An example of an inhomogeneous manifold with injectivity radius the same for all points can be constructed as follows. Recall that a point of the
 26 Jan 2011 The compactness is irrelevant; i.e if it is true for compact manifolds then the same is true for complete ones. (The same proof as in comact case
 2 Dec 2005 CURVATURE AND INJECTIVITY RADIUS ESTIMATES For example, almost all complex surfaces .. To see this, modify the definition of ?(p)
 This is a glossary of some terms used in Riemannian geometry and metric geometry — it doesn't cover the terminology of differential topology. The following articles may also be useful; they either contain specialised vocabulary or provide more detailed expositions of the definitions given . Injectivity radius The injectivity radius at a point p of a Riemannian manifold
 In order to define the injectivity radius, we consider the ball B(0,r) := {v ? TpM . This example suggests that we may be able to find estimates for the shortest
 We survey results about the injectivity radius and sphere the- orems, from the early .. (iii) Even worse, in dimension 7, the Aloff–Wallach examples [1975] described . proof of Theorem 1.9 has led to a fruitful definition of what a critical point.
      
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