Growth conditions for conformal transformations preserving Riemannian completeness

Details Growth conditions for conformal transformations preserving Riemannian completeness Growth conditions for conformal transformations preserving Riemannian completeness

2012-02-24

arxiv.org/abs/1202.5437v1

Mathematics

Differential Geometry

5 pages. The main theorem is already contained in: A. Dirmeier, M. Plaue and M. Scherfner: Growth Conditions, Riemannian Compl

Scientific paper

For a complete Riemannian metric, a pointwise conformal transformation may
lead to a complete or incomplete transformed Riemannian metric, depending on
the behavior of the conformal factor. We establish conditions on the growth of
the conformal factor towards the infinity of the Riemannian metric, such that
the conformally transformed Riemannian metric remains complete.

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