# ON THE EXISTENCE OF A STRAIGHT LINE By

@inproceedings{Ohtsuka2008ONTE, title={ON THE EXISTENCE OF A STRAIGHT LINE By}, author={Fumiko Ohtsuka}, year={2008} }

element of M and expressed as C(M)=\ GdMThe influence of total curvature JM of such an M have been investigated by many people. The pioneering work on total curvature was done by Cohn-Vossen in [1], which stated that if M admits total curvature, then C(M)^L.2tzX{M), where %(M) is the Euler characteristicof M. He also proved in [2] that if a Riemannian plane M (i.e. M is a complete Riemannian manifold homeomorphic to R2) admits total curvature and if there exists a straight line on M, then C(M… CONTINUE READING