Results in Mathematics

, Volume 43, Issue 3–4, pp 205–234 | Cite as

Geometric Structures as Determined by the Volume of Generalized Geodesic Balls



Several authors have studied the Taylor expansion for the volume of geodesic balls under the exponential mapping of an analytic Riemannian manifold \( (M, {\cal G}) \). A more general structure \( (M, D{\cal G}) \), where D is a torsion-free and Ricci-symmetric connection, appears in several geometric situations. We study the Taylor expansion in this case, where all metric notions are Riemannian, while now the exponential mapping is induced from the connection D. We give many applications, in particular in different hypersurface theories.


Geodesic Ball Elliptic Paraboloid Difference Tensor Affine Differential Geometry Weingarten Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Birkhäuser Verlag, Basel 2003

Authors and Affiliations

  1. 1.Faculty Of MathematicsUniversity Of BelgradeBelgradeYugoslavia
  2. 2.MA 8-3, TU BerlinMathematisches InstitutBerlinGermany

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