On geodesic balls in Riemannian manifolds endowed with symmetric connection
by
Mirjana Djoric
University of Belgrade, Yugoslavia
Coauthors: Neda Bokan (University of Belgrade, Yugoslavia), Udo Simon (Technical University Berlin, Germany)

Oral Communication

Let (M, g, D) be an n-dimensional analytic manifold, endowed with a Riemannian metric g and a torsion-free connection D. We introduce the following notions: Consider a sphere and a ball of small radius r, both defined in terms of the metric in the tangent space M_m, and consider their images under the exponential map defined in terms of the connection D; we call the images a small D-geodesic sphere and a D-geodesic ball on M. We calculate the Taylor expansion for the volume of the D-geodesic ball centered at m in M with radius r. Finally, we study the geometry of hypersurface immersed in an affine space, determined by the volume of small D-geodesic balls for different normalizations, where D is either the induced or the conormal connection of the hypersurface.

Date received: June 6, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafh-11.